Tudor, Ciprian A. The overdamped generalized Langevin equation with Hermite noise. (English) Zbl 1522.60059 Fract. Calc. Appl. Anal. 26, No. 3, 1082-1103 (2023). MSC: 60H15 60H07 65C30 60G22 PDFBibTeX XMLCite \textit{C. A. Tudor}, Fract. Calc. Appl. Anal. 26, No. 3, 1082--1103 (2023; Zbl 1522.60059) Full Text: DOI
Li, Qiang; Wu, Xu Existence and asymptotic behavior of square-mean \(S\)-asymptotically periodic solutions for fractional stochastic evolution equation with delay. (English) Zbl 1511.60097 Fract. Calc. Appl. Anal. 26, No. 2, 718-750 (2023). MSC: 60H15 47D06 34G20 46T20 PDFBibTeX XMLCite \textit{Q. Li} and \textit{X. Wu}, Fract. Calc. Appl. Anal. 26, No. 2, 718--750 (2023; Zbl 1511.60097) Full Text: DOI
Moulay Hachemi, Rahma Yasmina; Øksendal, Bernt The fractional stochastic heat equation driven by time-space white noise. (English) Zbl 1511.35371 Fract. Calc. Appl. Anal. 26, No. 2, 513-532 (2023). MSC: 35R11 35R60 35K05 60H15 60H40 26A33 PDFBibTeX XMLCite \textit{R. Y. Moulay Hachemi} and \textit{B. Øksendal}, Fract. Calc. Appl. Anal. 26, No. 2, 513--532 (2023; Zbl 1511.35371) Full Text: DOI
Zili, Mounir; Zougar, Eya Mixed stochastic heat equation with fractional Laplacian and gradient perturbation. (English) Zbl 1503.60086 Fract. Calc. Appl. Anal. 25, No. 2, 783-802 (2022). MSC: 60H15 60G15 35R11 35R60 35K05 26A33 PDFBibTeX XMLCite \textit{M. Zili} and \textit{E. Zougar}, Fract. Calc. Appl. Anal. 25, No. 2, 783--802 (2022; Zbl 1503.60086) Full Text: DOI
Arab, Zineb; El-Borai, Mahmoud Mohamed Wellposedness and stability of fractional stochastic nonlinear heat equation in Hilbert space. (English) Zbl 1503.35246 Fract. Calc. Appl. Anal. 25, No. 5, 2020-2039 (2022). MSC: 35R11 35R60 26A33 35K05 47N20 PDFBibTeX XMLCite \textit{Z. Arab} and \textit{M. M. El-Borai}, Fract. Calc. Appl. Anal. 25, No. 5, 2020--2039 (2022; Zbl 1503.35246) Full Text: DOI
Ji, Un Cig; Lee, Mi Ra; Ma, Peng Cheng Fractional Langevin type equations for white noise distributions. (English) Zbl 1498.60298 Fract. Calc. Appl. Anal. 24, No. 4, 1160-1192 (2021). MSC: 60H40 60H15 26A33 PDFBibTeX XMLCite \textit{U. C. Ji} et al., Fract. Calc. Appl. Anal. 24, No. 4, 1160--1192 (2021; Zbl 1498.60298) Full Text: DOI
Japundžić, Miloš; Rajter-Ćirić, Danijela Fractional nonlinear stochastic heat equation with variable thermal conductivity. (English) Zbl 1474.60162 Fract. Calc. Appl. Anal. 23, No. 6, 1762-1782 (2020). MSC: 60H15 35R11 46F30 60G22 PDFBibTeX XMLCite \textit{M. Japundžić} and \textit{D. Rajter-Ćirić}, Fract. Calc. Appl. Anal. 23, No. 6, 1762--1782 (2020; Zbl 1474.60162) Full Text: DOI
Atanacković, Teodor; Pilipović, Stevan; Seleši, Dora Wave propagation dynamics in a fractional Zener model with stochastic excitation. (English) Zbl 1488.35324 Fract. Calc. Appl. Anal. 23, No. 6, 1570-1604 (2020). MSC: 35L05 26A33 35R11 35R60 60G15 74D05 74J05 82D30 PDFBibTeX XMLCite \textit{T. Atanacković} et al., Fract. Calc. Appl. Anal. 23, No. 6, 1570--1604 (2020; Zbl 1488.35324) Full Text: DOI
Tomovski, Živorad; Dubbeldam, Johan L. A.; Korbel, Jan Applications of Hilfer-Prabhakar operator to option pricing financial model. (English) Zbl 1474.91213 Fract. Calc. Appl. Anal. 23, No. 4, 996-1012 (2020). MSC: 91G20 35Q91 35R11 91G30 PDFBibTeX XMLCite \textit{Ž. Tomovski} et al., Fract. Calc. Appl. Anal. 23, No. 4, 996--1012 (2020; Zbl 1474.91213) Full Text: DOI
Ascione, Giacomo; Mishura, Yuliya; Pirozzi, Enrica Time-changed fractional Ornstein-Uhlenbeck process. (English) Zbl 1450.60030 Fract. Calc. Appl. Anal. 23, No. 2, 450-483 (2020). MSC: 60G22 26A33 35Q84 42A38 42B10 60H10 82C31 PDFBibTeX XMLCite \textit{G. Ascione} et al., Fract. Calc. Appl. Anal. 23, No. 2, 450--483 (2020; Zbl 1450.60030) Full Text: DOI arXiv
D’Ovidio, Mirko; Vitali, Silvia; Sposini, Vittoria; Sliusarenko, Oleksii; Paradisi, Paolo; Castellani, Gastone; Pagnini, Gianni Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion. (English) Zbl 1436.60041 Fract. Calc. Appl. Anal. 21, No. 5, 1420-1435 (2018). MSC: 60G22 65C30 91B70 60J60 34A08 60J70 PDFBibTeX XMLCite \textit{M. D'Ovidio} et al., Fract. Calc. Appl. Anal. 21, No. 5, 1420--1435 (2018; Zbl 1436.60041) Full Text: DOI arXiv
Hausenblas, Erika; Kovács, Mihály Global solutions to stochastic Volterra equations driven by Lévy noise. (English) Zbl 1436.60064 Fract. Calc. Appl. Anal. 21, No. 5, 1170-1202 (2018). MSC: 60H15 60G57 45D05 PDFBibTeX XMLCite \textit{E. Hausenblas} and \textit{M. Kovács}, Fract. Calc. Appl. Anal. 21, No. 5, 1170--1202 (2018; Zbl 1436.60064) Full Text: DOI arXiv
Yan, Litan; Yin, Xiuwei Large deviation principle for a space-time fractional stochastic heat equation with fractional noise. (English) Zbl 1398.60047 Fract. Calc. Appl. Anal. 21, No. 2, 462-485 (2018). MSC: 60F10 60H15 60G22 35R11 PDFBibTeX XMLCite \textit{L. Yan} and \textit{X. Yin}, Fract. Calc. Appl. Anal. 21, No. 2, 462--485 (2018; Zbl 1398.60047) Full Text: DOI
Umarov, Sabir; Daum, Fred; Nelson, Kenric Fractional generalizations of Zakai equation and some solution methods. (English) Zbl 1401.60070 Fract. Calc. Appl. Anal. 21, No. 2, 336-353 (2018). MSC: 60G35 35R11 93E10 60G05 35Q84 PDFBibTeX XMLCite \textit{S. Umarov} et al., Fract. Calc. Appl. Anal. 21, No. 2, 336--353 (2018; Zbl 1401.60070) Full Text: DOI Link
Górska, Katarzyna; Lattanzi, Ambra; Dattoli, Giuseppe Mittag-Leffler function and fractional differential equations. (English) Zbl 1390.35398 Fract. Calc. Appl. Anal. 21, No. 1, 220-236 (2018). MSC: 35R11 35Q84 60G52 PDFBibTeX XMLCite \textit{K. Górska} et al., Fract. Calc. Appl. Anal. 21, No. 1, 220--236 (2018; Zbl 1390.35398) Full Text: DOI arXiv
Umarov, Sabir Fractional Fokker-Planck-Kolmogorov equations associated with SDEs on a bounded domain. (English) Zbl 1374.60109 Fract. Calc. Appl. Anal. 20, No. 5, 1281-1304 (2017). MSC: 60H10 35K20 35S11 PDFBibTeX XMLCite \textit{S. Umarov}, Fract. Calc. Appl. Anal. 20, No. 5, 1281--1304 (2017; Zbl 1374.60109) Full Text: DOI arXiv
Magdziarz, Marcin; Zorawik, Tomasz Densities of scaling limits of coupled continuous time random walks. (English) Zbl 1354.26011 Fract. Calc. Appl. Anal. 19, No. 6, 1488-1506 (2016). MSC: 26A33 60G52 60E07 PDFBibTeX XMLCite \textit{M. Magdziarz} and \textit{T. Zorawik}, Fract. Calc. Appl. Anal. 19, No. 6, 1488--1506 (2016; Zbl 1354.26011) Full Text: DOI
Khalil, Marwa; Tudor, Ciprian; Zili, Mounir On the Lamperti transform of the fractional Brownian sheet. (English) Zbl 1355.60051 Fract. Calc. Appl. Anal. 19, No. 6, 1466-1487 (2016). MSC: 60G22 60H05 60H10 60G18 60G10 60G15 PDFBibTeX XMLCite \textit{M. Khalil} et al., Fract. Calc. Appl. Anal. 19, No. 6, 1466--1487 (2016; Zbl 1355.60051) Full Text: DOI
Pagnini, Gianni; Paradisi, Paolo A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation. (English) Zbl 1341.60073 Fract. Calc. Appl. Anal. 19, No. 2, 408-440 (2016). MSC: 60H30 35R11 60G15 60G22 60J60 60G10 60G18 60G20 26A33 82C31 PDFBibTeX XMLCite \textit{G. Pagnini} and \textit{P. Paradisi}, Fract. Calc. Appl. Anal. 19, No. 2, 408--440 (2016; Zbl 1341.60073) Full Text: DOI arXiv
Tudor, Ciprian A. Recent developments on stochastic heat equation with additive fractional-colored noise. (English) Zbl 1322.60124 Fract. Calc. Appl. Anal. 17, No. 1, 224-246 (2014). MSC: 60H15 60G22 60F05 60H05 60G18 PDFBibTeX XMLCite \textit{C. A. Tudor}, Fract. Calc. Appl. Anal. 17, No. 1, 224--246 (2014; Zbl 1322.60124) Full Text: DOI
Stern, Robin; Effenberger, Frederic; Fichtner, Horst; Schäfer, Tobias The space-fractional diffusion-advection equation: analytical solutions and critical assessment of numerical solutions. (English) Zbl 1312.35188 Fract. Calc. Appl. Anal. 17, No. 1, 171-190 (2014). MSC: 35R11 33C60 60J60 65C05 65M06 35R60 PDFBibTeX XMLCite \textit{R. Stern} et al., Fract. Calc. Appl. Anal. 17, No. 1, 171--190 (2014; Zbl 1312.35188) Full Text: DOI arXiv
Tudor, Ciprian; Zili, Mounir Covariance measure and stochastic heat equation with fractional noise. (English) Zbl 1306.60094 Fract. Calc. Appl. Anal. 17, No. 3, 807-826 (2014). MSC: 60H15 60G22 60H05 60F05 PDFBibTeX XMLCite \textit{C. Tudor} and \textit{M. Zili}, Fract. Calc. Appl. Anal. 17, No. 3, 807--826 (2014; Zbl 1306.60094) Full Text: DOI
Umarov, Sabir; Daum, Frederick; Nelson, Kenric Fractional generalizations of filtering problems and their associated fractional Zakai equations. (English) Zbl 1306.60081 Fract. Calc. Appl. Anal. 17, No. 3, 745-764 (2014). MSC: 60H10 60G51 60H05 35S10 26A33 PDFBibTeX XMLCite \textit{S. Umarov} et al., Fract. Calc. Appl. Anal. 17, No. 3, 745--764 (2014; Zbl 1306.60081) Full Text: DOI arXiv Link
Michelitsch, Thomas; Maugin, Gérard; Nowakowski, Andrzej; Nicolleau, Franck; Rahman, Mujibur The fractional Laplacian as a limiting case of a self-similar spring model and applications to \(n\)-dimensional anomalous diffusion. (English) Zbl 1314.35209 Fract. Calc. Appl. Anal. 16, No. 4, 827-859 (2013). MSC: 35R11 28A80 35Q84 60E07 82C31 60G18 60J60 PDFBibTeX XMLCite \textit{T. Michelitsch} et al., Fract. Calc. Appl. Anal. 16, No. 4, 827--859 (2013; Zbl 1314.35209) Full Text: DOI
Guo, Peng; Zeng, Caibin; Li, Changpin; Chen, YangQuan Numerics for the fractional Langevin equation driven by the fractional Brownian motion. (English) Zbl 1312.34093 Fract. Calc. Appl. Anal. 16, No. 1, 123-141 (2013). MSC: 34F05 34A08 60G22 65C30 65L12 PDFBibTeX XMLCite \textit{P. Guo} et al., Fract. Calc. Appl. Anal. 16, No. 1, 123--141 (2013; Zbl 1312.34093) Full Text: DOI
Zeng, Caibin; Chen, Yangquan; Yang, Qigui The fBm-driven Ornstein-Uhlenbeck process: probability density function and anomalous diffusion. (English) Zbl 1274.60127 Fract. Calc. Appl. Anal. 15, No. 3, 479-492 (2012). MSC: 60G22 26A33 35R60 60H15 35Q84 PDFBibTeX XMLCite \textit{C. Zeng} et al., Fract. Calc. Appl. Anal. 15, No. 3, 479--492 (2012; Zbl 1274.60127) Full Text: DOI
Sandev, Trifce; Metzler, Ralf; Tomovski, Živorad Velocity and displacement correlation functions for fractional generalized Langevin equations. (English) Zbl 1274.82045 Fract. Calc. Appl. Anal. 15, No. 3, 426-450 (2012). MSC: 82C31 33E12 34A08 PDFBibTeX XMLCite \textit{T. Sandev} et al., Fract. Calc. Appl. Anal. 15, No. 3, 426--450 (2012; Zbl 1274.82045) Full Text: DOI
Bishwal, Jaya P. N. Minimum contrast estimation in fractional Ornstein-Uhlenbeck process: continuous and discrete sampling. (English) Zbl 1273.62056 Fract. Calc. Appl. Anal. 14, No. 3, 375-410 (2011). MSC: 62F12 62M05 60F05 60F10 60G22 60H10 PDFBibTeX XMLCite \textit{J. P. N. Bishwal}, Fract. Calc. Appl. Anal. 14, No. 3, 375--410 (2011; Zbl 1273.62056) Full Text: DOI
Hahn, Marjorie; Umarov, Sabir Fractional Fokker-Planck-Kolmogorov type equations and their associated stochastic differential equations. (English) Zbl 1273.35293 Fract. Calc. Appl. Anal. 14, No. 1, 56-79 (2011). MSC: 35R11 35-02 35R60 60H10 82C31 35Q84 PDFBibTeX XMLCite \textit{M. Hahn} and \textit{S. Umarov}, Fract. Calc. Appl. Anal. 14, No. 1, 56--79 (2011; Zbl 1273.35293) Full Text: DOI Link