Edit Profile (opens in new tab) Metzler, Ralf Co-Author Distance Author ID: metzler.ralf Published as: Metzler, Ralf; Metzler, R. External Links: ORCID Documents Indexed: 89 Publications since 1995, including 6 Additional arXiv Preprints 6 Contributions as Editor · 1 Further Contribution Co-Authors: 112 Co-Authors with 91 Joint Publications 2,578 Co-Co-Authors all top 5 Co-Authors 3 single-authored 31 Chechkin, Aleksei V. 13 Sandev, Trifce 9 Klafter, Joseph 9 Nonnenmacher, Theo F. 6 Oshanin, Gleb 5 Cherstvy, Andrey G. 5 Godec, Aljaž 5 Sokolov, Igor’ Mikhaĭlovich 5 Xu, Yong 4 Dybiec, Bartłomiej 4 Jeon, Jae-Hyung 4 Tomovski, Živorad 3 Awad, Emad S. 3 Gonchar, Vsevolod Yu. 3 Grebenkov, Denis S. 3 Kantz, Holger 3 Kurths, Jürgen 3 Lomholt, Michael A. 3 Padash, Amin 3 Palyulin, Vladimir V. 3 Shokri, Babak 3 Tejedor, Vincent 2 Aghion, Erez 2 Bénichou, Olivier 2 Blumen, Alexander 2 Capała, Karol 2 Iomin, Alexander 2 Kocarev, Ljupco 2 Li, Yongge 2 Lim, Swee Cheng 2 Magdziarz, Marcin 2 Mutothya, Nicholas Mwilu 2 Schiessel, Helmut 2 Seno, Flavio 2 Sposini, Vittoria 2 Tanatarov, Leonid V. 2 Teomy, Eial 2 Thapa, Samudrajit 2 Voituriez, Raphaël 2 Wang, Wei 2 West, Bruce J. 2 Zan, Wanrong 1 Assaf, Michael 1 Bakk, Audun 1 Banik, Suman Kumar 1 Barkai, Eli 1 Blavatska, Viktoria 1 Burov, Stanislav 1 Butzer, Paul Leo 1 Chaudhury, Pinaki 1 Compte, Albert 1 Delvenne, Jean-Charles 1 Di Bello, C. 1 Dollinger, Jürgen W. 1 Domazetoski, Viktor 1 Douglas, Jack F. 1 Estrada, Ernesto 1 García-March, Miguel Ángel 1 Gerhold, Stefan 1 Glöckle, Walter G. 1 Grigolini, Paolo 1 Gudowska-Nowak, Ewa 1 Guggenberger, Tobias 1 Hanke, Andreas 1 Hartmann, Alexander K. 1 Hatano, Naomichi 1 Hilfer, Rudolf 1 Holcman, David 1 Kim, Yeongjin 1 Klages, Rainer 1 Koren, Tal 1 Krapf, Diego 1 Krüsemann, Henning 1 Lemaitre, Elisabeth 1 Lewenstein, Maciej 1 Li, Hua 1 Lindenberg, Katja 1 Liu, Xianbin 1 Lukat, N. 1 Mackey, Michael Charles 1 Manzo, Carlo 1 Marinari, Enzo 1 Mateos, José L. 1 Mattos, T. G. 1 Mejía-Monasterio, Carlos 1 Muñoz-Gil, Gorka 1 Nathan, Ran 1 Palmowski, Zbigniew 1 Park, Seongyu 1 Pavlyukevich, Ilya 1 Redner, Sidney 1 Riascos, Alejandro P. 1 Safdari, Hadiseh 1 Schad, Michaela 1 Schaub, Michael T. 1 Schehr, Grégory 1 Schulz, Johannes H. P. 1 Schwarzl, Maria 1 Selhuber-Unkel, C. 1 Ślęzak, Jakub Karol ...and 20 more Co-Authors all top 5 Serials 39 Journal of Physics A: Mathematical and Theoretical 8 Journal of Physics A: Mathematical and General 5 Chaos, Solitons and Fractals 5 Fractional Calculus & Applied Analysis 5 Journal of Statistical Mechanics: Theory and Experiment 2 Journal of Mathematical Physics 2 Fractals 2 Chaos 2 New Journal of Physics 2 Mathematical Modelling of Natural Phenomena 1 International Journal of Plasticity 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Physica A 1 Physics Letters. A 1 Physics Reports 1 Proceedings of the National Academy of Sciences of the United States of America 1 Physica Scripta 1 Journal of Theoretical Biology 1 Journal of Complex Networks all top 5 Fields 51 Probability theory and stochastic processes (60-XX) 47 Statistical mechanics, structure of matter (82-XX) 16 Partial differential equations (35-XX) 11 Biology and other natural sciences (92-XX) 10 Real functions (26-XX) 7 Dynamical systems and ergodic theory (37-XX) 6 General and overarching topics; collections (00-XX) 6 Special functions (33-XX) 4 Ordinary differential equations (34-XX) 4 Statistics (62-XX) 4 Quantum theory (81-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Integral equations (45-XX) 1 Numerical analysis (65-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Relativity and gravitational theory (83-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 81 Publications have been cited 4,301 times in 3,387 Documents Cited by ▼ Year ▼ Applications of fractional calculus in physics. Zbl 0998.26002 2,794 2000 The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Zbl 0984.82032 Metzler, Ralf; Klafter, Joseph 2,473 2000 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. Zbl 1075.82018 Metzler, Ralf; Klafter, Joseph 739 2004 Fractional dynamics. Recent advances. Zbl 1238.93005 104 2012 The generalized Cattaneo equation for the description of anomalous transport processes. Zbl 0941.82046 Compte, Albert; Metzler, Ralf 99 1997 Generalized viscoelastic models: Their fractional equations with solutions. Zbl 0921.73154 Schiessel, H.; Metzler, R.; Blumen, A.; Nonnenmacher, T. F. 91 1995 First-passage phenomena and their applications. Zbl 1291.00067 81 2014 Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative. Zbl 1301.82042 Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad 67 2011 Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Zbl 1338.60199 Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf 42 2015 First passage and arrival time densities for Lévy flights and the failure of the method of images. Zbl 1049.60090 Chechkin, Aleksei V.; Metzler, Ralf; Gonchar, Vsevolod Y.; Klafter, Joseph; Tanatarov, Leonid V. 39 2003 On the Riemann-Liouville fractional calculus and some recent applications. Zbl 0868.26004 Nonnenmacher, Theo F.; Metzler, Ralf 38 1995 Lévy flights in a steep potential well. Zbl 1157.82305 Chechkin, Aleksei V.; Gonchar, Vsevolod Yu.; Klafter, Joseph; Metzler, Ralf; Tanatarov, Leonid V. 34 2004 From continuous time random walks to the generalized diffusion equation. Zbl 1499.35683 Sandev, Trifce; Metzler, Ralf; Chechkin, Aleksei 31 2018 Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Zbl 1090.74673 Metzler, Ralf; Nonnenmacher, Theo F. 23 2003 Aging and nonergodicity beyond the Khinchin theorem. Zbl 1205.82113 Burov, S.; Metzler, R.; Barkai, E. 22 2010 Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise. Zbl 1291.82097 Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad 20 2014 Beyond monofractional kinetics. Zbl 1374.45016 Sandev, Trifce; Sokolov, Igor M.; Metzler, Ralf; Chechkin, Aleksei 19 2017 First passage time statistics for two-channel diffusion. Zbl 1459.82230 Godec, Aljaž; Metzler, Ralf 18 2017 Anomalous diffusion in correlated continuous time random walks. Zbl 1189.82082 Tejedor, Vincent; Metzler, Ralf 16 2010 Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time. Zbl 1519.82101 Wang, Wei; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Thapa, Samudrajit; Seno, Flavio; Liu, Xianbin; Metzler, Ralf 15 2020 Comb model with slow and ultraslow diffusion. Zbl 1386.60287 Sandev, T.; Iomin, A.; Kantz, H.; Metzler, R.; Chechkin, A. 14 2016 Velocity and displacement correlation functions for fractional generalized Langevin equations. Zbl 1274.82045 Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad 14 2012 From the Langevin equation to the fractional Fokker-Planck equation. Zbl 0972.82065 Metzler, Ralf; Klafter, Joseph 13 2000 Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion. Zbl 1457.82343 Metzler, Ralf 13 2019 First passage statistics for diffusing diffusivity. Zbl 1422.82019 Sposini, Vittoria; Chechkin, Aleksei; Metzler, Ralf 13 2019 First-passage properties of asymmetric Lévy flights. Zbl 1509.60106 Padash, Amin; Chechkin, Aleksei V.; Dybiec, Bartlomiej; Pavlyukevich, Ilya; Shokri, Babak; Metzler, Ralf 13 2019 Quantifying the non-ergodicity of scaled Brownian motion. Zbl 1329.82096 Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Thiel, Felix; Sokolov, Igor M.; Metzler, Ralf 12 2015 Localisation and universal fluctuations in ultraslow diffusion processes. Zbl 1305.60074 Godec, Aljaž; Chechkin, Aleksei V.; Barkai, Eli; Kantz, Holger; Metzler, Ralf 12 2014 Resetting dynamics in a confining potential. Zbl 1519.82098 Singh, R. K.; Metzler, R.; Sandev, T. 12 2020 Some fundamental aspects of Lévy flights. Zbl 1142.82341 Metzler, Ralf; Chechkin, Aleksei V.; Gonchar, Vsevolod Yu.; Klafter, Joseph 11 2007 Non-uniqueness of the first passage time density of Lévy random processes. Zbl 1071.60033 Sokolov, Igor M.; Metzler, Ralf 10 2004 Applications of fractional calculus techniques to problems in biophysics. Zbl 0984.92005 Nonnenmacher, Theo F.; Metzler, Ralf 9 2000 Ageing and confinement in non-ergodic heterogeneous diffusion processes. Zbl 1351.37018 Cherstvy, Andrey G.; Chechkin, Aleksei V.; Metzler, Ralf 9 2014 Analysis of short subdiffusive time series: scatter of the time-averaged mean-squared displacement. Zbl 1192.82037 Jeon, Jae-Hyung; Metzler, Ralf 9 2010 Heterogeneous diffusion with stochastic resetting. Zbl 1505.82046 Sandev, Trifce; Domazetoski, Viktor; Kocarev, Ljupco; Metzler, Ralf; Chechkin, Aleksei 9 2022 Preface: new trends in first-passage methods and applications in the life sciences and engineering. Zbl 07642059 9 2020 Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion. Zbl 1220.82054 Tejedor, V.; Bénichou, O.; Metzler, Ralf; Voituriez, R. 8 2011 Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias. Zbl 1456.82784 Palyulin, Vladimir V.; Chechkin, Aleksei V.; Metzler, Ralf 8 2014 Search reliability and search efficiency of combined Lévy-Brownian motion: long relocations mingled with thorough local exploration. Zbl 1350.60044 Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf 8 2016 Backbone diffusion and first-passage dynamics in a comb structure with confining branches under stochastic resetting. Zbl 1519.60100 Singh, R. K.; Sandev, T.; Iomin, A.; Metzler, R. 8 2021 A single predator charging a herd of prey: effects of self volume and predator-prey decision-making. Zbl 1342.92200 Schwarzl, Maria; Godec, Aljaz; Oshanin, Gleb; Metzler, Ralf 7 2016 Crossover dynamics from superdiffusion to subdiffusion: models and solutions. Zbl 1439.35519 Awad, Emad; Metzler, Ralf 7 2020 Correlated continuous time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics. Zbl 1305.60032 Schulz, Johannes H. P.; Chechkin, Aleksei V.; Metzler, Ralf 7 2013 Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. Zbl 0872.60097 Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.; Mackey, Michael C. 6 1996 Ageing first passage time density in continuous time random walks and quenched energy landscapes. Zbl 1372.60065 Krüsemann, Henning; Godec, Aljaž; Metzler, Ralf 6 2015 Correlated continuous-time random walks – scaling limits and Langevin picture. Zbl 1459.82270 Magdziarz, Marcin; Metzler, Ralf; Szczotka, Wladyslaw; Zebrowski, Piotr 6 2012 Random multi-hopper model: super-fast random walks on graphs. Zbl 1462.05328 Estrada, Ernesto; Delvenne, Jean-Charles; Hatano, Naomichi; Mateos, José L.; Metzler, Ralf; Riascos, Alejandro P.; Schaub, Michael T. 6 2018 First-passage problem for stochastic differential equations with combined parametric Gaussian and Lévy white noises via path integral method. Zbl 07503736 Zan, Wanrong; Xu, Yong; Metzler, Ralf; Kurths, Jürgen 6 2021 Bi-asymptotic fractals: Fractals between lower and upper bounds. Zbl 0930.37005 Dollinger, Jürgen W.; Metzler, Ralf; Nonnenmacher, Theo F. 5 1998 Active transport improves the precision of linear long distance molecular signalling. Zbl 1353.82063 Godec, Aljaž; Metzler, Ralf 5 2016 Fractional diffusion: Exact representations of spectral functions. Zbl 1001.82538 Metzler, R.; Nonnenmacher, T. F. 5 1997 Exact first-passage time distributions for three random diffusivity models. Zbl 1519.60077 Grebenkov, Denis S.; Sposini, Vittoria; Metzler, Ralf; Oshanin, Gleb; Seno, Flavio 5 2021 Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions. Zbl 1519.60116 Guggenberger, Tobias; Chechkin, Aleksei; Metzler, Ralf 5 2021 Encounter distribution of two random walkers on a finite one-dimensional interval. Zbl 1225.82028 Tejedor, Vincent; Schad, Michaela; Bénichou, Olivier; Voituriez, Raphael; Metzler, Ralf 4 2011 Lévy meets Boltzmann: strange initial conditions for Brownian and fractional Fokker-Planck equations. Zbl 0979.82050 Metzler, Ralf; Klafter, Joseph 4 2001 Bubble dynamics in DNA. Zbl 1073.92502 Hanke, Andreas; Metzler, Ralf 4 2003 Conservative random walks in confining potentials. Zbl 1422.60074 Dybiec, Bartłomiej; Capała, Karol; Chechkin, Aleksei V.; Metzler, Ralf 4 2019 Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity. Zbl 1456.82763 Cherstvy, Andrey G.; Metzler, Ralf 4 2015 First passage time moments of asymmetric Lévy flights. Zbl 1519.60049 Padash, Amin; Chechkin, Aleksei V.; Dybiec, Bartłomiej; Magdziarz, Marcin; Shokri, Babak; Metzler, Ralf 4 2020 Stochastic dynamics driven by combined Lévy-Gaussian noise: fractional Fokker-Planck-Kolmogorov equation and solution. Zbl 1519.60064 Zan, Wanrong; Xu, Yong; Kurths, Jürgen; Chechkin, Aleksei V.; Metzler, Ralf 4 2020 A remark on the Neugebauer-Meinel rotating disk solution of general relativity. Zbl 1072.83502 Metzler, R. 3 1996 “Fractional tuning” of the Riccati equation. Zbl 0913.34011 Metzler, R.; Glöckle, W. G.; Nonnenmacher, T. F.; West, B. J. 3 1997 Bulk-mediated surface diffusion on a cylinder in the fast exchange limit. Zbl 1267.82112 Chechkin, A. V.; Zaid, I. M.; Lomholt, M. A.; Sokolov, I. M.; Metzler, R. 3 2013 Classification of anomalous diffusion in animal movement data using power spectral analysis. Zbl 1511.92099 Vilk, Ohad; Aghion, Erez; Nathan, Ran; Toledo, Sivan; Metzler, Ralf; Assaf, Michael 3 2022 Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise. Zbl 1519.60119 Mutothya, Nicholas Mwilu; Xu, Yong; Li, Yongge; Metzler, Ralf 3 2021 Time averaging, ageing and delay analysis of financial time series. Zbl 1516.91042 Cherstvy, Andrey G.; Vinod, Deepak; Aghion, Erez; Chechkin, Aleksei V.; Metzler, Ralf 3 2017 And did he search for you, and could not find you? Zbl 1186.68149 Metzler, Ralf; Koren, Tal; van den Broek, Bram; Wuite, Gijs J. L.; Lomholt, Michael A. 2 2009 Anomalous diffusion and fractional transport equations. Zbl 1297.35277 Metzler, Ralf; Jeon, Jae-Hyung 2 2012 Conformational properties of complex polymers: rosette versus star-like structures. Zbl 1330.92093 Blavatska, V.; Metzler, R. 2 2015 Speeding up the first-passage for subdiffusion by introducing a finite potential barrier. Zbl 1285.82046 Palyulin, Vladimir V.; Metzler, Ralf 2 2014 Closed-form multi-dimensional solutions and asymptotic behaviours for subdiffusive processes with crossovers. II: Accelerating case. Zbl 1506.35259 Awad, Emad; Metzler, Ralf 2 2022 Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers. I: Retarding case. Zbl 1506.35260 Awad, Emad; Sandev, Trifce; Metzler, Ralf; Chechkin, Aleksei 2 2021 Preface: Marian Smoluchowski’s 1916 paper – a century of inspiration. Zbl 1375.01039 1 2017 Lévy noise-driven escape from arctangent potential wells. Zbl 1451.34078 Capała, Karol; Padash, Amin; Chechkin, Aleksei V.; Shokri, Babak; Metzler, Ralf; Dybiec, Bartłomiej 1 2020 Bayesian inference of scaled versus fractional Brownian motion. Zbl 1506.62361 Thapa, Samudrajit; Park, Seongyu; Kim, Yeongjin; Jeon, Jae-Hyung; Metzler, Ralf; Lomholt, Michael A. 1 2022 Fractional characteristic functions, and a fractional calculus approach for moments of random variables. Zbl 1503.26013 Tomovski, Živorad; Metzler, Ralf; Gerhold, Stefan 1 2022 Transport in exclusion processes with one-step memory: density dependence and optimal acceleration. Zbl 1504.82046 Teomy, Eial; Metzler, Ralf 1 2019 Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher’s equation, anomalous crossovers and resetting. Zbl 1508.60069 Sandev, Trifce; Kocarev, Ljupco; Metzler, Ralf; Chechkin, Aleksei 1 2022 Preface: Characterisation of physical processes from anomalous diffusion data. Zbl 07657031 1 2023 The role of ergodicity in anomalous stochastic processes: analysis of single-particle trajectories. Zbl 1267.82101 Metzler, Ralf; Jeon, Jae-Hyung 1 2012 Correlations and transport in exclusion processes with general finite memory. Zbl 1457.82269 Teomy, Eial; Metzler, Ralf 1 2019 Preface: Characterisation of physical processes from anomalous diffusion data. Zbl 07657031 1 2023 Heterogeneous diffusion with stochastic resetting. Zbl 1505.82046 Sandev, Trifce; Domazetoski, Viktor; Kocarev, Ljupco; Metzler, Ralf; Chechkin, Aleksei 9 2022 Classification of anomalous diffusion in animal movement data using power spectral analysis. Zbl 1511.92099 Vilk, Ohad; Aghion, Erez; Nathan, Ran; Toledo, Sivan; Metzler, Ralf; Assaf, Michael 3 2022 Closed-form multi-dimensional solutions and asymptotic behaviours for subdiffusive processes with crossovers. II: Accelerating case. Zbl 1506.35259 Awad, Emad; Metzler, Ralf 2 2022 Bayesian inference of scaled versus fractional Brownian motion. Zbl 1506.62361 Thapa, Samudrajit; Park, Seongyu; Kim, Yeongjin; Jeon, Jae-Hyung; Metzler, Ralf; Lomholt, Michael A. 1 2022 Fractional characteristic functions, and a fractional calculus approach for moments of random variables. Zbl 1503.26013 Tomovski, Živorad; Metzler, Ralf; Gerhold, Stefan 1 2022 Stochastic dynamics with multiplicative dichotomic noise: heterogeneous telegrapher’s equation, anomalous crossovers and resetting. Zbl 1508.60069 Sandev, Trifce; Kocarev, Ljupco; Metzler, Ralf; Chechkin, Aleksei 1 2022 Backbone diffusion and first-passage dynamics in a comb structure with confining branches under stochastic resetting. Zbl 1519.60100 Singh, R. K.; Sandev, T.; Iomin, A.; Metzler, R. 8 2021 First-passage problem for stochastic differential equations with combined parametric Gaussian and Lévy white noises via path integral method. Zbl 07503736 Zan, Wanrong; Xu, Yong; Metzler, Ralf; Kurths, Jürgen 6 2021 Exact first-passage time distributions for three random diffusivity models. Zbl 1519.60077 Grebenkov, Denis S.; Sposini, Vittoria; Metzler, Ralf; Oshanin, Gleb; Seno, Flavio 5 2021 Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions. Zbl 1519.60116 Guggenberger, Tobias; Chechkin, Aleksei; Metzler, Ralf 5 2021 Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise. Zbl 1519.60119 Mutothya, Nicholas Mwilu; Xu, Yong; Li, Yongge; Metzler, Ralf 3 2021 Closed-form multi-dimensional solutions and asymptotic behaviors for subdiffusive processes with crossovers. I: Retarding case. Zbl 1506.35260 Awad, Emad; Sandev, Trifce; Metzler, Ralf; Chechkin, Aleksei 2 2021 Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time. Zbl 1519.82101 Wang, Wei; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Thapa, Samudrajit; Seno, Flavio; Liu, Xianbin; Metzler, Ralf 15 2020 Resetting dynamics in a confining potential. Zbl 1519.82098 Singh, R. K.; Metzler, R.; Sandev, T. 12 2020 Preface: new trends in first-passage methods and applications in the life sciences and engineering. Zbl 07642059 9 2020 Crossover dynamics from superdiffusion to subdiffusion: models and solutions. Zbl 1439.35519 Awad, Emad; Metzler, Ralf 7 2020 First passage time moments of asymmetric Lévy flights. Zbl 1519.60049 Padash, Amin; Chechkin, Aleksei V.; Dybiec, Bartłomiej; Magdziarz, Marcin; Shokri, Babak; Metzler, Ralf 4 2020 Stochastic dynamics driven by combined Lévy-Gaussian noise: fractional Fokker-Planck-Kolmogorov equation and solution. Zbl 1519.60064 Zan, Wanrong; Xu, Yong; Kurths, Jürgen; Chechkin, Aleksei V.; Metzler, Ralf 4 2020 Lévy noise-driven escape from arctangent potential wells. Zbl 1451.34078 Capała, Karol; Padash, Amin; Chechkin, Aleksei V.; Shokri, Babak; Metzler, Ralf; Dybiec, Bartłomiej 1 2020 Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion. Zbl 1457.82343 Metzler, Ralf 13 2019 First passage statistics for diffusing diffusivity. Zbl 1422.82019 Sposini, Vittoria; Chechkin, Aleksei; Metzler, Ralf 13 2019 First-passage properties of asymmetric Lévy flights. Zbl 1509.60106 Padash, Amin; Chechkin, Aleksei V.; Dybiec, Bartlomiej; Pavlyukevich, Ilya; Shokri, Babak; Metzler, Ralf 13 2019 Conservative random walks in confining potentials. Zbl 1422.60074 Dybiec, Bartłomiej; Capała, Karol; Chechkin, Aleksei V.; Metzler, Ralf 4 2019 Transport in exclusion processes with one-step memory: density dependence and optimal acceleration. Zbl 1504.82046 Teomy, Eial; Metzler, Ralf 1 2019 Correlations and transport in exclusion processes with general finite memory. Zbl 1457.82269 Teomy, Eial; Metzler, Ralf 1 2019 From continuous time random walks to the generalized diffusion equation. Zbl 1499.35683 Sandev, Trifce; Metzler, Ralf; Chechkin, Aleksei 31 2018 Random multi-hopper model: super-fast random walks on graphs. Zbl 1462.05328 Estrada, Ernesto; Delvenne, Jean-Charles; Hatano, Naomichi; Mateos, José L.; Metzler, Ralf; Riascos, Alejandro P.; Schaub, Michael T. 6 2018 Beyond monofractional kinetics. Zbl 1374.45016 Sandev, Trifce; Sokolov, Igor M.; Metzler, Ralf; Chechkin, Aleksei 19 2017 First passage time statistics for two-channel diffusion. Zbl 1459.82230 Godec, Aljaž; Metzler, Ralf 18 2017 Time averaging, ageing and delay analysis of financial time series. Zbl 1516.91042 Cherstvy, Andrey G.; Vinod, Deepak; Aghion, Erez; Chechkin, Aleksei V.; Metzler, Ralf 3 2017 Preface: Marian Smoluchowski’s 1916 paper – a century of inspiration. Zbl 1375.01039 1 2017 Comb model with slow and ultraslow diffusion. Zbl 1386.60287 Sandev, T.; Iomin, A.; Kantz, H.; Metzler, R.; Chechkin, A. 14 2016 Search reliability and search efficiency of combined Lévy-Brownian motion: long relocations mingled with thorough local exploration. Zbl 1350.60044 Palyulin, Vladimir V.; Chechkin, Aleksei V.; Klages, Rainer; Metzler, Ralf 8 2016 A single predator charging a herd of prey: effects of self volume and predator-prey decision-making. Zbl 1342.92200 Schwarzl, Maria; Godec, Aljaz; Oshanin, Gleb; Metzler, Ralf 7 2016 Active transport improves the precision of linear long distance molecular signalling. Zbl 1353.82063 Godec, Aljaž; Metzler, Ralf 5 2016 Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel. Zbl 1338.60199 Sandev, Trifce; Chechkin, Aleksei; Kantz, Holger; Metzler, Ralf 42 2015 Quantifying the non-ergodicity of scaled Brownian motion. Zbl 1329.82096 Safdari, Hadiseh; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Thiel, Felix; Sokolov, Igor M.; Metzler, Ralf 12 2015 Ageing first passage time density in continuous time random walks and quenched energy landscapes. Zbl 1372.60065 Krüsemann, Henning; Godec, Aljaž; Metzler, Ralf 6 2015 Ergodicity breaking, ageing, and confinement in generalized diffusion processes with position and time dependent diffusivity. Zbl 1456.82763 Cherstvy, Andrey G.; Metzler, Ralf 4 2015 Conformational properties of complex polymers: rosette versus star-like structures. Zbl 1330.92093 Blavatska, V.; Metzler, R. 2 2015 First-passage phenomena and their applications. Zbl 1291.00067 81 2014 Correlation functions for the fractional generalized Langevin equation in the presence of internal and external noise. Zbl 1291.82097 Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad 20 2014 Localisation and universal fluctuations in ultraslow diffusion processes. Zbl 1305.60074 Godec, Aljaž; Chechkin, Aleksei V.; Barkai, Eli; Kantz, Holger; Metzler, Ralf 12 2014 Ageing and confinement in non-ergodic heterogeneous diffusion processes. Zbl 1351.37018 Cherstvy, Andrey G.; Chechkin, Aleksei V.; Metzler, Ralf 9 2014 Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias. Zbl 1456.82784 Palyulin, Vladimir V.; Chechkin, Aleksei V.; Metzler, Ralf 8 2014 Speeding up the first-passage for subdiffusion by introducing a finite potential barrier. Zbl 1285.82046 Palyulin, Vladimir V.; Metzler, Ralf 2 2014 Correlated continuous time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics. Zbl 1305.60032 Schulz, Johannes H. P.; Chechkin, Aleksei V.; Metzler, Ralf 7 2013 Bulk-mediated surface diffusion on a cylinder in the fast exchange limit. Zbl 1267.82112 Chechkin, A. V.; Zaid, I. M.; Lomholt, M. A.; Sokolov, I. M.; Metzler, R. 3 2013 Fractional dynamics. Recent advances. Zbl 1238.93005 104 2012 Velocity and displacement correlation functions for fractional generalized Langevin equations. Zbl 1274.82045 Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad 14 2012 Correlated continuous-time random walks – scaling limits and Langevin picture. Zbl 1459.82270 Magdziarz, Marcin; Metzler, Ralf; Szczotka, Wladyslaw; Zebrowski, Piotr 6 2012 Anomalous diffusion and fractional transport equations. Zbl 1297.35277 Metzler, Ralf; Jeon, Jae-Hyung 2 2012 The role of ergodicity in anomalous stochastic processes: analysis of single-particle trajectories. Zbl 1267.82101 Metzler, Ralf; Jeon, Jae-Hyung 1 2012 Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative. Zbl 1301.82042 Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad 67 2011 Residual mean first-passage time for jump processes: theory and applications to Lévy flights and fractional Brownian motion. Zbl 1220.82054 Tejedor, V.; Bénichou, O.; Metzler, Ralf; Voituriez, R. 8 2011 Encounter distribution of two random walkers on a finite one-dimensional interval. Zbl 1225.82028 Tejedor, Vincent; Schad, Michaela; Bénichou, Olivier; Voituriez, Raphael; Metzler, Ralf 4 2011 Aging and nonergodicity beyond the Khinchin theorem. Zbl 1205.82113 Burov, S.; Metzler, R.; Barkai, E. 22 2010 Anomalous diffusion in correlated continuous time random walks. Zbl 1189.82082 Tejedor, Vincent; Metzler, Ralf 16 2010 Analysis of short subdiffusive time series: scatter of the time-averaged mean-squared displacement. Zbl 1192.82037 Jeon, Jae-Hyung; Metzler, Ralf 9 2010 And did he search for you, and could not find you? Zbl 1186.68149 Metzler, Ralf; Koren, Tal; van den Broek, Bram; Wuite, Gijs J. L.; Lomholt, Michael A. 2 2009 Some fundamental aspects of Lévy flights. Zbl 1142.82341 Metzler, Ralf; Chechkin, Aleksei V.; Gonchar, Vsevolod Yu.; Klafter, Joseph 11 2007 The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. Zbl 1075.82018 Metzler, Ralf; Klafter, Joseph 739 2004 Lévy flights in a steep potential well. Zbl 1157.82305 Chechkin, Aleksei V.; Gonchar, Vsevolod Yu.; Klafter, Joseph; Metzler, Ralf; Tanatarov, Leonid V. 34 2004 Non-uniqueness of the first passage time density of Lévy random processes. Zbl 1071.60033 Sokolov, Igor M.; Metzler, Ralf 10 2004 First passage and arrival time densities for Lévy flights and the failure of the method of images. Zbl 1049.60090 Chechkin, Aleksei V.; Metzler, Ralf; Gonchar, Vsevolod Y.; Klafter, Joseph; Tanatarov, Leonid V. 39 2003 Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. Zbl 1090.74673 Metzler, Ralf; Nonnenmacher, Theo F. 23 2003 Bubble dynamics in DNA. Zbl 1073.92502 Hanke, Andreas; Metzler, Ralf 4 2003 Lévy meets Boltzmann: strange initial conditions for Brownian and fractional Fokker-Planck equations. Zbl 0979.82050 Metzler, Ralf; Klafter, Joseph 4 2001 Applications of fractional calculus in physics. Zbl 0998.26002 2,794 2000 The random walk’s guide to anomalous diffusion: A fractional dynamics approach. Zbl 0984.82032 Metzler, Ralf; Klafter, Joseph 2,473 2000 From the Langevin equation to the fractional Fokker-Planck equation. Zbl 0972.82065 Metzler, Ralf; Klafter, Joseph 13 2000 Applications of fractional calculus techniques to problems in biophysics. Zbl 0984.92005 Nonnenmacher, Theo F.; Metzler, Ralf 9 2000 Bi-asymptotic fractals: Fractals between lower and upper bounds. Zbl 0930.37005 Dollinger, Jürgen W.; Metzler, Ralf; Nonnenmacher, Theo F. 5 1998 The generalized Cattaneo equation for the description of anomalous transport processes. Zbl 0941.82046 Compte, Albert; Metzler, Ralf 99 1997 Fractional diffusion: Exact representations of spectral functions. Zbl 1001.82538 Metzler, R.; Nonnenmacher, T. F. 5 1997 “Fractional tuning” of the Riccati equation. Zbl 0913.34011 Metzler, R.; Glöckle, W. G.; Nonnenmacher, T. F.; West, B. J. 3 1997 Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential. Zbl 0872.60097 Vlad, Marcel Ovidiu; Metzler, Ralf; Nonnenmacher, Theo F.; Mackey, Michael C. 6 1996 A remark on the Neugebauer-Meinel rotating disk solution of general relativity. Zbl 1072.83502 Metzler, R. 3 1996 Generalized viscoelastic models: Their fractional equations with solutions. Zbl 0921.73154 Schiessel, H.; Metzler, R.; Blumen, A.; Nonnenmacher, T. F. 91 1995 On the Riemann-Liouville fractional calculus and some recent applications. Zbl 0868.26004 Nonnenmacher, Theo F.; Metzler, Ralf 38 1995 all cited Publications top 5 cited Publications all top 5 Cited by 4,254 Authors 83 Wang, Hong 58 Liu, Fawang 47 Deng, Weihua 44 Meerschaert, Mark Marvin 40 Zheng, Xiangcheng 38 Metzler, Ralf 37 Sandev, Trifce 35 Anh, Vo V. 31 Wei, Ting 30 Băleanu, Dumitru I. 30 Turner, Ian William 27 Kaminski Lenzi, Ervin 26 Li, Changpin 24 Chechkin, Aleksei V. 24 Dehghan Takht Fooladi, Mehdi 24 Sun, Hongguang 23 Ahmad, Bashir 23 Chen, Yangquan 23 Karniadakis, George Em 21 Burrage, Kevin 21 Zhou, Zhi 20 Abbaszadeh, Mostafa 20 Povstenko, Yuriy Z. 19 Eliazar, Iddo I. 18 Tarasov, Vasily E. 17 Al-saedi, Ahmed Eid Salem 17 Chen, Wen 17 Dybiec, Bartłomiej 17 Fu, Hongfei 17 Mainardi, Francesco 17 Pagnini, Gianni 17 Tomovski, Živorad 17 Yamamoto, Masahiro 16 Duan, Jinqiao 16 Jiang, Xiaoyun 16 Magdziarz, Marcin 15 Feng, Libo 15 Henry, Bruce I. 15 Jin, Bangti 15 Sun, Zhizhong 15 Trujillo, Juan J. 15 Vougalter, Vitali 15 Xu, Yong 14 Grebenkov, Denis S. 14 Jia, Jinhong 14 Mohebbi, Akbar 14 Yang, Xiao-Jun 14 Zhou, Yong 13 Bäumer, Boris 13 D’Elia, Marta 13 Iomin, Alexander 13 Leonenko, Nikolai N. 13 Nguyen Huy Tuan 13 Scheffler, Hans-Peter 13 Wang, Yuanming 13 Wu, Guocheng 13 Zheng, Guanghui 12 Ding, Hengfei 12 Du, Ning 12 Du, Qiang 12 Ge, Fudong 12 Khaliq, Abdul Q. M. 12 Liu, Yanqin 12 Peng, Jigen 12 Saxena, Ram Kishore 12 Sousa, Ercília 12 Umarov, Sabir R. 12 Zayernouri, Mohsen 12 Zhang, Yong 11 Angstmann, Christopher N. 11 Barkai, Eli 11 Cattani, Carlo 11 Furati, Khaled M. 11 Gorenflo, Rudolf 11 Płociniczak, Łukasz 11 Sun, Liangliang 11 Teng, Kaimin 11 Yang, Zhiwei 11 Zeng, Fanhai 11 Zheng, Liancun 10 Atangana, Abdon 10 Gu, Xian-Ming 10 Gunzburger, Max D. 10 Li, Can 10 Liang, Yingjie 10 Liu, Huan 10 Lu, Shujuan 10 Nepomnyashchy, Alexander A. 10 O’Regan, Donal 10 Qi, Haitao 10 Wu, Yujiang 10 Zacher, Rico 10 Zhang, Zhimin 9 Balachandran, Krishnan 9 Chen, Changming 9 Cui, Mingrong 9 de Oliveira, Edmundo Capelas 9 Gajda, Janusz 9 Garra, Roberto 9 Kirane, Mokhtar ...and 4,154 more Authors all top 5 Cited in 420 Serials 140 Journal of Physics A: Mathematical and Theoretical 139 Physica A 137 Computers & Mathematics with Applications 133 Fractional Calculus & Applied Analysis 107 Applied Mathematics and Computation 94 Chaos, Solitons and Fractals 92 Journal of Computational Physics 84 Communications in Nonlinear Science and Numerical Simulation 82 Journal of Computational and Applied Mathematics 70 Journal of Statistical Physics 70 Journal of Statistical Mechanics: Theory and Experiment 66 Journal of Mathematical Physics 64 Journal of Scientific Computing 53 Advances in Difference Equations 51 Applied Numerical Mathematics 46 International Journal of Computer Mathematics 42 Journal of Mathematical Analysis and Applications 39 Mathematical Methods in the Applied Sciences 39 Applied Mathematical Modelling 35 Numerical Algorithms 35 Abstract and Applied Analysis 35 Chaos 34 Computational and Applied Mathematics 31 Numerical Methods for Partial Differential Equations 29 Nonlinear Dynamics 28 Applicable Analysis 27 Inverse Problems 27 SIAM Journal on Scientific Computing 27 Fractals 26 Advances in Mathematical Physics 25 SIAM Journal on Numerical Analysis 25 Applied Mathematics Letters 25 Mathematical Modelling of Natural Phenomena 24 Journal of Differential Equations 21 Journal of Applied Mathematics and Computing 19 Mathematical Problems in Engineering 19 Boundary Value Problems 18 Computer Methods in Applied Mechanics and Engineering 17 Mathematics and Computers in Simulation 17 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 17 Discrete and Continuous Dynamical Systems. Series B 16 Physics Letters. A 16 Bulletin of Mathematical Biology 16 Stochastic Processes and their Applications 16 The European Physical Journal B. Condensed Matter and Complex Systems 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 SIAM Journal on Mathematical Analysis 14 Journal of Inverse and Ill-Posed Problems 14 Journal of Evolution Equations 14 Inverse Problems in Science and Engineering 14 Journal of Function Spaces 13 Physica D 13 Engineering Analysis with Boundary Elements 12 Acta Mechanica 12 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 12 Mediterranean Journal of Mathematics 11 Advances in Computational Mathematics 11 Journal of Mathematical Chemistry 11 Discrete and Continuous Dynamical Systems. Series S 11 AIMS Mathematics 10 BIT 10 Journal of Vibration and Control 10 Communications on Pure and Applied Analysis 10 Multiscale Modeling & Simulation 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Mathematics 9 SIAM Journal on Applied Mathematics 9 Nonlinear Analysis. Real World Applications 9 Journal of Theoretical Biology 9 Fractional Differential Calculus 9 East Asian Journal on Applied Mathematics 9 International Journal of Applied and Computational Mathematics 8 Journal of Functional Analysis 8 Journal of Optimization Theory and Applications 8 Proceedings of the American Mathematical Society 8 Statistics & Probability Letters 8 Journal of Nonlinear Science 8 Cybernetics and Systems Analysis 8 Discrete Dynamics in Nature and Society 8 International Journal of Nonlinear Sciences and Numerical Simulation 8 Communications on Applied Mathematics and Computation 7 International Journal of Modern Physics B 7 Theoretical and Mathematical Physics 7 Mathematics of Computation 7 Meccanica 7 Computational Mechanics 7 Lobachevskii Journal of Mathematics 7 Nonlinear Analysis. Modelling and Control 7 Inverse Problems and Imaging 6 Computer Physics Communications 6 International Journal of Theoretical Physics 6 The Annals of Probability 6 Numerical Functional Analysis and Optimization 6 SIAM Journal on Control and Optimization 6 Journal of Integral Equations and Applications 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 6 Communications in Statistics. Theory and Methods 6 Potential Analysis 6 NoDEA. Nonlinear Differential Equations and Applications 6 Bulletin des Sciences Mathématiques ...and 320 more Serials all top 5 Cited in 51 Fields 1,872 Partial differential equations (35-XX) 1,112 Numerical analysis (65-XX) 704 Real functions (26-XX) 640 Probability theory and stochastic processes (60-XX) 518 Statistical mechanics, structure of matter (82-XX) 463 Ordinary differential equations (34-XX) 195 Fluid mechanics (76-XX) 190 Integral equations (45-XX) 184 Biology and other natural sciences (92-XX) 176 Operator theory (47-XX) 142 Special functions (33-XX) 115 Mechanics of deformable solids (74-XX) 88 Calculus of variations and optimal control; optimization (49-XX) 84 Dynamical systems and ergodic theory (37-XX) 82 Quantum theory (81-XX) 82 Systems theory; control (93-XX) 71 Classical thermodynamics, heat transfer (80-XX) 63 Statistics (62-XX) 59 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 58 Integral transforms, operational calculus (44-XX) 39 Measure and integration (28-XX) 36 Approximations and expansions (41-XX) 36 Functional analysis (46-XX) 33 Harmonic analysis on Euclidean spaces (42-XX) 26 Information and communication theory, circuits (94-XX) 25 Global analysis, analysis on manifolds (58-XX) 24 Combinatorics (05-XX) 24 Computer science (68-XX) 24 Mechanics of particles and systems (70-XX) 23 Linear and multilinear algebra; matrix theory (15-XX) 23 Optics, electromagnetic theory (78-XX) 20 Geophysics (86-XX) 18 Difference and functional equations (39-XX) 18 Operations research, mathematical programming (90-XX) 6 General and overarching topics; collections (00-XX) 6 Number theory (11-XX) 5 Sequences, series, summability (40-XX) 4 History and biography (01-XX) 4 Functions of a complex variable (30-XX) 4 Potential theory (31-XX) 4 Relativity and gravitational theory (83-XX) 4 Astronomy and astrophysics (85-XX) 3 Abstract harmonic analysis (43-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Mathematics education (97-XX) 1 Field theory and polynomials (12-XX) 1 Nonassociative rings and algebras (17-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) Citations by Year