## Fractals

### Complex Geometry, Patterns, and Scaling in Nature and Society

 Short Title: Fractals Publisher: World Scientific, Singapore ISSN: 0218-348X; 1793-6543/e Online: https://www.worldscientific.com/loi/fractals
 Documents Indexed: 1,435 Publications (since 1993) References Indexed: 1,158 Publications with 32,539 References.
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### Citations contained in zbMATH Open

689 Publications have been cited 3,363 times in 2,288 Documents Cited by Year
Estimators for long-range dependence: An empirical study. Zbl 0864.62061
1995
The relationship between fractional calculus and fractals. Zbl 0877.28009
Tatom, Frank B.
1995
Distributed order fractional sub-diffusion. Zbl 1083.60066
Naber, Mark
2004
Bivariate fractal interpolation functions on grids. Zbl 1088.28502
Dalla, Leoni
2002
The study of bivariate fractal interpolation functions and creation of fractal interpolated surfaces. Zbl 0908.65005
Xie, Heping; Sun, Hongquan
1997
Hidden variable bivariate fractal interpolation surfaces. Zbl 1046.28004
Chand, A. K. B.; Kapoor, G. P.
2003
On the Riemann-Liouville fractional calculus and some recent applications. Zbl 0868.26004
Nonnenmacher, Theo F.; Metzler, Ralf
1995
Average geodesic distance of Sierpinski gasket and Sierpinski networks. Zbl 1375.28020
Wang, Songjing; Yu, Zhouyu; Xi, Lifeng
2017
Calculus on fractal subsets of real line. I: Formulation. Zbl 1173.28005
Parvate, Abhay; Gangal, A. D.
2009
First-order network coherence and eigentime identity on the weighted Cayley networks. Zbl 1421.05083
Dai, Meifeng; Wang, Xiaoqian; Zong, Yue; Zou, Jiahui; Chen, Yufei; Su, Weiyi
2017
On Hadamard fractional calculus. Zbl 1371.26009
Ma, Li; Li, Changpin
2017
A generalized Mandelbrot set for bicomplex numbers. Zbl 0969.37021
Rochon, Dominic
2000
Cooperative strategies in formation of complex bacterial patterns. Zbl 0869.92002
Ben-Jacob, Eshel; Shochet, Ofer; Cohen, Inon; Tenenbaum, Adam; Czirók, Andras; Vicsek, Tamas
1995
Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform. Zbl 1083.65005
2004
On fractional relaxation. Zbl 1140.82315
Hilfer, R.
2003
Fractal bases of $$L_p$$ spaces. Zbl 1251.28009
Navascués, M. A.
2012
Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302
Falconer, Kenneth; Miao, Jun
2007
A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004
Barnsley, Michael; Hutchinson, John; Stenflo, Örjan
2005
Multifractal cascade dynamics and turbulent intermittency. Zbl 0927.76044
Schertzer, D.; Lovejoy, S.; Schmitt, F.; Chigirinskaya, Y.; Marsan, D.
1997
Hidden variable vector valued fractal interpolation functions. Zbl 1100.41011
Bouboulis, P.; Dalla, L.
2005
Topological structure of self-similar sets. Zbl 1075.28005
Luo, Jun; Rao, Hui; Tan, Bo
2002
Analysis of fractional differential equations with multi-orders. Zbl 1176.34008
Deng, Weihua; Li, Changpin; Guo, Qian
2007
Exact solutions for a class of fractal time random walks. Zbl 0881.60066
Hilfer, R.
1995
On the dimension of self-similar sets. Zbl 1088.28504
Simon, Károly; Solomyak, Boris
2002
Modifications at large distances from fractional and fractal arguments. Zbl 1196.28014
2010
Certain integral inequalities considering generalized $$m$$-convexity on fractal sets and their applications. Zbl 1434.28018
2019
Foundations of fractional dynamics. Zbl 0870.58041
Hilfer, R.
1995
Analysis of $$\mathbb{C}$$-plane fractal images from $$z \leftarrow z^{\alpha} + c$$ for $$(\alpha < 0)$$. Zbl 1211.37059
Wang, Xingyuan; Liu, Xiangdong; Zhu, Weiyong; Gu, Shusheng
2000
Average geodesic distance of Sierpinski carpet. Zbl 1432.28015
Zhao, Luming; Wang, Songjing; Xi, Lifeng
2017
Nonextensive thermostatics and fractals. Zbl 0870.58098
Tsallis, Constantino
1995
Dimension analysis of continuous functions with unbounded variation. Zbl 1371.28012
Wang, Jun; Yao, Kui
2017
Vibration spectra of finitely ramifield, symmetric fractals. Zbl 1160.28302
Bajorin, N.; Chen, T.; Dagan, A.; Emmons, C.; Hussein, M.; Khalil, M.; Mody, P.; Steinhurst, B.; Teplyaev, A.
2008
Some further extensions considering discrete proportional fractional operators. Zbl 07490662
Rashid, Saima; Sultana, Sobia; Karaca, Yeliz; Khalid, Aasma; Chu, Yu-Ming
2022
Average distance of self-similar fractal trees. Zbl 1432.28007
Li, Tingting; Jiang, Kan; Xi, Lifeng
2018
Normal families of bicomplex holomorphic functions. Zbl 1230.30032
Charak, K. S.; Rochon, D.; Sharma, N.
2009
Calculus on fractal subsets of real line. II: Conjugacy with ordinary calculus. Zbl 1252.28005
Parvate, Abhay; Gangal, A. D.
2011
Fractal image compression. Zbl 0903.68211
Fisher, Yuval
1994
Box dimensions of {$$\alpha$$}-fractal functions. Zbl 1354.28002
Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A.
2016
Central limit theorem for the log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context. Zbl 1141.62073
Moulines, E.; Roueff, F.; Taqqu, Murad S.
2007
Path properties of the linear multifractional stable motion. Zbl 1304.28010
2005
On a generalized Fatou-Julia theorem in multicomplex spaces. Zbl 1177.30068
Garant-Pelletier, V.; Rochon, D.
2009
Estimation and simulation of fractal stochastic point processes. Zbl 0881.60044
Lowen, Steven B.; Teich, Malvin C.
1995
Calculus on fractal curves in $$\mathbb{R}^{n}$$. Zbl 1217.28014
Parvate, Abhay; Satin, Seema; Gangal, A. D.
2011
On stability of fractal interpolation. Zbl 0974.28003
Feng, Zhigang; Xie, Heping
1998
Fractal geometry of financial time series. Zbl 0869.62073
Evertsz, Carl J. G.
1995
Explicit construction of operator scaling Gaussian random fields. Zbl 1233.60027
Clausel, M.; Vedel, B.
2011
Multifractal cross-correlation analysis based on statistical moments. Zbl 1272.28013
Wang, Jing; Shang, Pengjian; Ge, Weijie
2012
Analysis, synthesis, and estimation of fractal-rate stochastic point processes. Zbl 0907.62093
Thurner, Stefan; Lowen, Steven B.; Feurstein, Markus C.; Heneghan, Conor; Feichtinger, Hans G.; Teich, Malvin C.
1997
A technique in the topology of connected self-similar tiles. Zbl 1304.28009
Ngai, Sze-Man; Tang, Tai-Man
2004
On a generalized Fatou-Julia theorem. Zbl 1041.37023
Rochon, Dominic
2003
$$1/f$$ noise in a traffic model. Zbl 0906.90072
Takayasu, Misako; Takayasu, Hideki
1993
Definition, properties and wavelet analysis of multiscale fractional Brownian motion. Zbl 1142.60329
Bardet, Jean-Marc; Bertrand, Pierre
2007
A remark on Wang’s fractal variational principle. Zbl 1434.35267
Wang, Kang-Le; He, Chun-Hui
2019
Green’s functions on fractals. Zbl 0983.31005
Kigami, Jun; Sheldon, Daniel R.; Strichartz, Robert S.
2000
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
2003
On the Assouad dimension of graph directed Moran fractals. Zbl 1222.28017
Olsen, L.
2011
Natural cubic spline coalescence hidden variable fractal interpolation surfaces. Zbl 1250.28004
Chand, A. K. B.
2012
Fractal modeling of speech signals. Zbl 1126.94308
Lévy Véhel, Jacques; Daoudi, Khalid; Lutton, Evelyne
1994
Cantor-type sets in hyperbolic numbers. Zbl 1357.28008
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016
Construction and analysis of a special one-dimensional continuous function. Zbl 1371.28011
Wang, J.; Yao, Kui
2017
On smoothness for a class of fractal interpolation surfaces. Zbl 1302.37020
Wang, Hong-Yong
2006
Lipschitz equivalence of McMullen sets. Zbl 1290.28012
Li, Boming; Li, Wenxia; Miao, Jun Jie
2013
The multifractal dimension functions of homogeneous Moran measure. Zbl 1165.28005
Xiao, Jiaqing; Wu, Min
2008
An analysis of U.S. stock price behavior using wavelets. Zbl 0877.90027
Ramsey, James B.; Usikov, Daniel; Zaslavsky, George M.
1995
Generalizations of Newton’s method. Zbl 1046.37027
Gilbert, William J.
2001
Vector random fields with long-range dependence. Zbl 1232.60038
Ma, Chunsheng
2011
Study on the fractal and chaotic features of the Shanghai composite index. Zbl 1250.91084
Wen, Fenghua; Li, Zhong; Xie, Chaohua; Shaw, David
2012
Fractal interpolation functions on post critically finite self-similar sets. Zbl 1196.28019
Ruan, Huo-Jun
2010
Fractal dimension of certain continuous functions of unbounded variation. Zbl 1371.28005
Liang, Y. S.; Su, W. Y.
2017
Spectral analysis for weighted iterated triangulations of graphs. Zbl 1432.35058
Chen, Yufei; Dai, Meifeng; Wang, Xiaoqian; Sun, Yu; Su, Weiyi
2018
Fractal approaches in signal processing. Zbl 0867.94005
Lévy-Véhel, Jacques
1995
On the automatic selection of the onset of scaling. Zbl 1056.62102
Veitch, Darryl; Abry, Patrice; Taqqu, Murad S.
2003
Some results of convergence of cubic spline fractal interpolation functions. Zbl 1053.41013
Navascués, M. Antonia; Sebastián, M. Victoria
2003
Fractal description of anomalous diffusion in dynamical systems. Zbl 0901.58050
Klafter, J.; Zumofen, G.; Shlesinger, M. F.
1993
The fractal dimension of the Apollonian sphere packing. Zbl 0908.52008
Borkovec, M.; de Paris, W.; Peikert, R.
1994
Is network traffic self-similar or multifractal? Zbl 0908.60078
1997
Rényi function for multifractal random fields. Zbl 1278.28003
Leonenko, Nikolai N.; Shieh, Narn-Rueih
2013
The Hosoya index of graphs formed by a fractal graph. Zbl 1434.05039
Liu, Jia-bao; Zhao, Jing; Min, Jie; Cao, Jinde
2019
Eccentric distance sum of Sierpiński gasket and Sierpiński network. Zbl 1433.28009
Chen, Jin; He, Long; Wang, Qin
2019
Beyond classical multifractal analysis using wavelets: uncovering a multiplicative process hidden in the geometrical complexity of diffusion limited aggregates. Zbl 0901.58028
Arneodo, A.; Argoul, F.; Muzy, J. F.; Tabard, M.; Bacry, E.
1993
Fractal trigonometric polynomials for restricted range approximation. Zbl 1351.28009
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016
Construction of recurrent fractal interpolation surfaces with function scaling factors and estimation of box-counting dimension on rectangular grids. Zbl 1342.65085
Yun, Chol-Hui; Choi, Hui-Chol; O, Hyong-Chol
2015
The connection between the orders of $$p$$-adic calculus and the dimensions of the Weierstrass type function in local fields. Zbl 1136.37321
Qiu, Hua; Su, Weiyi
2007
Image compression using affine fractal interpolation on rectangular lattices. Zbl 1158.68051
Drakopoulos, V.; Bouboulis, P.; Theodoridis, S.
2006
A fractal approximation to periodicity. Zbl 1148.28010
Navascués, M. A.
2006
Numerical analysis on the Sierpinski gasket, with applications to Schrödinger equations, wave equation, and Gibbs’ phenomenon. Zbl 1304.28005
Coletta, Kevin; Dias, Kealey; Strichartz, Robert S.
2004
Hausdorff measure of Cartesian product of the ternary Cantor set. Zbl 1243.28003
Deng, Juan; Rao, Hui; Wen, Zhi-Ying
2012
An user intention mining model based on fractal time series pattern. Zbl 07468599
Wu, Shaofei
2020
A fractal model for water flow through unsaturated porous rocks. Zbl 1434.74085
Xiao, Boqi; Zhang, Xian; Wang, Wei; Long, Gongbo; Chen, Hanxin; Kang, Hao; Ren, Wen
2018
Asymptotic formula of average distances on fractal networks modeled by Sierpinski tetrahedron. Zbl 1434.28017
Deng, Juan; Wang, Qin
2019
Newton’s-type integral inequalities via local fractional integrals. Zbl 1434.26052
Iftikhar, Sabah; Kumam, Poom; Erden, Samet
2020
The effects of the Riemann-Liouville fractional integral on the box dimension of fractal graphs of Hölder continuous functions. Zbl 1434.26017
Wu, Junru
2020
Fractal networks on Sierpinski-type polygon. Zbl 1445.28019
Zeng, Cheng; Xue, Yumei; Zhou, Meng
2020
A new nonlinear fractal interpolation function. Zbl 1432.41001
Ri, Songil
2017
Comparison theorems for Caputo-Hadamard fractional differential equations. Zbl 1433.34012
Ma, Li
2019
Symmetry analysis, analytical solutions and conservation laws of a generalized KdV-Burgers-Kuramoto equation and its fractional version. Zbl 1482.35027
Wang, Gangwei
2021
Numerical solution of traveling waves in chemical kinetics: time-fractional fishers equations. Zbl 07507535
2022
Convergence of the Weierstrass-Mandelbrot process to fractional Brownian motion. Zbl 0976.60042
2000
The boundary of the attractor of a recurrent iterated function system. Zbl 1088.28503
Dekking, F. M.; van der Wal, P.
2002
Composed accelerated escape time algorithm to construct the general Mandelbrot sets. Zbl 1046.37030
Liu, Xiangdong; Zhu, Zhiliang; Wang, Guangxing; Zhu, Weiyong
2001
Some further extensions considering discrete proportional fractional operators. Zbl 07490662
Rashid, Saima; Sultana, Sobia; Karaca, Yeliz; Khalid, Aasma; Chu, Yu-Ming
2022
Numerical solution of traveling waves in chemical kinetics: time-fractional fishers equations. Zbl 07507535
2022
New developments in weighted $$n$$-fold type inequalities via discrete generalized $$\hat{\hbar}$$-proportional fractional operators. Zbl 07507540
Rashid, Saima; Abouelmagd, Elbaz I.; Sultana, Sobia; Chu, Yu-Ming
2022
Jensen-Mercer inequality and related results in the fractal sense with applications. Zbl 07490644
2022
Caputo type fractional operator applied to hepatitis B system. Zbl 07490659
Din, Anwarud; Li, Yongjin; Yusuf, Abdullahi; Ali, Aliyu Isa
2022
Impact of the same degenerate additive noise on a coupled system of fractional space diffusion equations. Zbl 1491.60105
Mohammed, Wael W.; Iqbal, Naveed
2022
Some recent developments on dynamical $$\hbar$$-discrete fractional type inequalities in the frame of nonsingular and nonlocal kernels. Zbl 1487.39011
Rashid, Saima; Abouelmagd, Elbaz I.; Khalid, Aasma; Farooq, Fozia Bashir; Chu, Yu-Ming
2022
On analysis of fractional order mathematical model of hepatitis B using Atangana-Baleanu Caputo (ABC) derivative. Zbl 1486.92219
Din, Anwarud; Li, Yongjin; Khan, Faiz Muhammad; Khan, Zia Ullah; Liu, Peijiang
2022
Shifted Legendre fractional pseudospectral differentiation matrices for solving fractional differential problems. Zbl 07490674
Abdelhakem, Mohamed; Abdelhamied, Dina; Alshehri, Maryam G.; El-Kady, Mamdouh
2022
Splines solutions of higher-order BVPs that arise in consistent magnetized force field. Zbl 07490679
Khalid, Aasma; Rehan, Akmal; Sooppy Nisar, Kottakkaran; Abdel-Aty, Abdel-Haleem; Zakarya, Mohammed
2022
Novel approach for fractal nonlinear oscillators with discontinuities by Fourier series. Zbl 07490695
Wang, Kang-Le
2022
A new $$(3+1)$$-Dimensional KdV equation and mkdv equation with their corresponding fractional forms. Zbl 07553222
Wang, Gangwei; Wazwaz, Abdul-Majid
2022
Riemann-Liouville fractional integro-differential equations with fractional nonlocal multi-point boundary conditions. Zbl 1486.45011
2022
Chaotic behavior of Bhalekar-Gejji dynamical system under Atangana-Baleanu fractal fractional operator. Zbl 07490641
2022
Analysis of time-fractional Kawahara equation under Mittag-Leffler power law. Zbl 1485.35403
Rahman, Mati Ur; Arfan, Muhammad; Deebani, Wejdan; Kumam, Poom; Shah, Zahir
2022
Result of local existence of solutions of nonlocal viscoelastic system with respect to the nonlinearity of source terms. Zbl 1485.35289
Boulaaras, Salah; Choucha, Abdelbaki; Ouchenane, Djamel; Alharbi, Asma; Abdalla, Mohamed
2022
An efficient analysis of difference equations with coherence fraction under the influence of boson interferometry. Zbl 1490.81127
2022
Dynamics of cooperative reactions based on chemical kinetics with reaction speed: a comparative analysis with singular and nonsingular kernels. Zbl 07490684
2022
Strange nonchaotic attractors in a periodically forced piecewise linear system with noise. Zbl 07490689
Li, Gaolei; Yue, Yuan; Grebogi, Celso; Li, Denghui; Xie, Jianhua
2022
Wada basins in an uncontrolled and controlled vibration isolation system. Zbl 07490690
Zhang, Yongxiang; Zhang, Fanhui
2022
A quaternionic fractional Borel-Pompeiu-type formula. Zbl 1486.30135
González-Cervantes, José Oscar; Bory-Reyes, Juan
2022
Research on the nonlinear vibration of carbon nanotube embedded in fractal medium. Zbl 07490702
Wang, Kang-Jia
2022
A novel permeability model in damaged tree-like bifurcating networks considering the influence of roughness. Zbl 07490714
Liu, Zhenjie; Gao, Jun; Xiao, Boqi; Cao, Jiyin; Fang, Jing; Liang, Mingchao; Long, Gongbo
2022
Fractal solitary wave solutions for fractal nonlinear dispersive Boussinesq-like models. Zbl 07553224
Wang, Kangle
2022
Fractal Hadamard-Mercer-type inequalities with applications. Zbl 07507539
2022
A nonlocal modeling for solving time fractional diffusion equation arising in fluid mechanics. Zbl 07578015
Hosseini, Vahid Reza; Rezazadeh, Arezou; Zheng, Hui; Zou, Wennan
2022
Symmetry analysis, analytical solutions and conservation laws of a generalized KdV-Burgers-Kuramoto equation and its fractional version. Zbl 1482.35027
Wang, Gangwei
2021
Complex fractional-order HIV diffusion model based on amplitude equations with Turing patterns and Turing instability. Zbl 1481.92036
Iqbal, Naveed; Karaca, Yeliz
2021
Tracking control and stabilization of a fractional financial risk system using novel active finite-time fault-tolerant controls. Zbl 1482.91215
Wang, Bo; Jahanshahi, Hadi; Bekiros, Stelios; Chu, Yu-Ming; Gómez-Aguilar, J. F.; Alsaadi, Fawaz E.; Alassafi, Madini O.
2021
Two-scale fractal theory for the population dynamics. Zbl 1481.92098
Anjum, Naveed; He, Chun-Hui; He, Ji-Huan
2021
A fractal-Monte Carlo approach to model oil and water two-phase seepage in low-permeability reservoirs with rough surfaces. Zbl 07465336
Su, Haibo; Zhang, Yidan; Xiao, Boqi; Huang, Xiaoming; Yu, Boming
2021
Optimal control of nonlinear time-delay fractional differential equations with Dickson polynomials. Zbl 1481.49032
Chen, Shu-Bo; Soradi-Zeid, Samaneh; Alipour, Maryam; Chu, Yu-Ming; Gómez-Aguilar, J. F.; Jahanshahi, Hadi
2021
Achieving more precise bounds based on double and triple integral as proposed by generalized proportional fractional operators in the Hilfer sense. Zbl 1481.26004
Al-Qurashi, Maysaa; Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming
2021
Variational principle and approximate solution for the generalized Burgers-Huxley equation with fractal derivative. Zbl 1482.35008
Wang, Kang-Jia
2021
A fractal model for predicting oxygen effective diffusivity of porous media with rough surfaces under dry and wet conditions. Zbl 07465418
Xiao, Boqi; Huang, Qiwen; Yu, Boming; Long, Gongbo; Chen, Hanxin
2021
Infinite number of parameter regions with fractal nonchaotic attractors in a piecewise map. Zbl 1489.37045
Cheng, Tao; Zhang, Yongxiang; Shen, Yunzhu
2021
Strange nonchaotic attractors and multistability in a two-degree-of-freedom quasiperiodically forced vibro-impact system. Zbl 1489.37046
Li, Gaolei; Yue, Yuan; Grebogi, Celso; Li, Denghui; Xie, Jianhua
2021
A fractal fractional model for cervical cancer due to human papillomavirus infection. Zbl 1489.37103
Akgül, A.; Ahmed, N.; Raza, A.; Iqbal, Z.; Rafiq, M.; Rehman, M. A.; Baleanu, D.
2021
Fractional Mayer neuro-swarm heuristic solver for multi-fractional order doubly singular model based on Lane-Emden equation. Zbl 1481.65104
Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru
2021
New computations of Ostrowski-type inequality pertaining to fractal style with applications. Zbl 1487.26029
Al Qurashi, Maysaa; Rashid, Saima; Khalid, Aasma; Karaca, Yeliz; Chu, Yu-Ming
2021
A fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media. Zbl 07465350
Xiao, Boqi; Huang, Qiwen; Chen, Hanxin; Chen, Xubing; Long, Gongbo
2021
Equivalent power-form representation of the fractal Toda oscillator. Zbl 1481.78022
Elías-Zúñiga, Alex; Palacios-Pineda, Luis Manuel; Jiménez-Cedeño, Isaac H.; Martínez-Romero, Oscar; Olvera Trejo, Daniel
2021
Fractal oscillation and its frequency-amplitude property. Zbl 1489.34014
He, Ji-Huan; Kou, Shuai-Jia; He, Chun-Hui; Zhang, Zuo-Wei; Gepreel, Khaled A.
2021
On the approximate solutions for a system of coupled Korteweg-de Vries equations with local fractional derivative. Zbl 07465612
Jafari, Hossein; Jassim, Hassan Kamil; Baleanu, Dumitru; Chu, Yu-Ming
2021
New multi-functional approach for $$\kappa$$th-order differentiability governed by fractional calculus via approximately generalized $$(\psi, \hbar)$$-convex functions in Hilbert space. Zbl 07465619
Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming
2021
Design of neuro-swarming heuristic solver for multi-pantograph singular delay differential equation. Zbl 1481.65098
Sabir, Zulqurnain; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Guirao, Juan L. G.
2021
A powerful iterative approach for quintic complex Ginzburg-Landau equation within the frame of fractional operator. Zbl 07465623
Yao, Shao-Wen; Ilhan, Esin; Veeresha, P.; Baskonus, Haci Mehmet
2021
Stability result and well-posedness for Timoshenko’s beam laminated with thermoelastic and past history. Zbl 1482.35040
Choucha, Abdelbaki; Boulaaras, Salah; Ouchenane, Djamel; Alkhalaf, Salem; Cherif, Bahri
2021
A fractal model for predicting the effective thermal conductivity of roughened porous media with microscale effect. Zbl 1481.80008
Xiao, Boqi; Zhang, Min; Chen, Hanxin; Cao, Jiyin; Long, Gongbo; Zhao, Zheng
2021
Information volume fractal dimension. Zbl 1491.94029
Gao, Qiuya; Wen, Tao; Deng, Yong
2021
Analysis of mixed Weyl-Marchaud fractional derivative and box dimensions. Zbl 1491.28003
Chandra, Subhash; Abbas, Syed
2021
Fractional order Volterra integro-differential equation with Mittag-Leffler kernel. Zbl 1482.65238
2021
A novel model for effective thermal conductivity of tree-like branching network with fractal roughened surfaces. Zbl 1482.80003
Liu, Yonghui; Li, Zihao; Xiao, Boqi; Chen, Hanxin; Long, Gongbo
2021
An investigation on spontaneous imbibition in tree-like branching network with fractal roughened surfaces. Zbl 1482.80005
Xiao, Boqi; Liu, Zhenjie; Zhang, Yidan; Liang, Mingchao; Long, Gongbo; Zhao, Zheng
2021
Maclaurin series method for fractal differential-difference models arising in coupled nonlinear optical waveguides. Zbl 1481.78012
Khan, Yasir
2021
Extensions of the Shannon entropy and the chaos game algorithm to hyperbolic numbers plane. Zbl 07465346
Téllez-Sánchez, G. Y.; Bory-Reyes, J.
2021
Upper box dimension of Riemann-Liouville fractional integral of fractal functions. Zbl 1487.28005
Liang, Y. S.; Wang, H. X.
2021
Modeling and analysis of novel COVID-19 under fractal-fractional derivative with case study of Malaysia. Zbl 1487.34100
2021
On the fractal variational principle for the telegraph equation. Zbl 1482.35005
He, Ji-Huan
2021
Fractal N/MEMS: from pull-in instability to pull-in stability. Zbl 1481.78002
Tian, Dan; Ain, Qura-Tul; Anjum, Naveed; He, Chun-Hui; Cheng, Bin
2021
Fractal Lakshmanan-Porsezian-Daniel model with different forms of nonlinearity and its novel soliton solutions. Zbl 1481.78023
Khan, Y.
2021
A study on gas drainage considering coupling process of fracture-pore microstructure and coal deformation. Zbl 07465387
Guannan, Liu; Dayu, Ye; Boming, Yu; Feng, Gao; Peijian, Chen
2021
Stability analysis of nonlinear uncertain fractional differential equations with Caputo derivative. Zbl 1487.34026
Lu, Ziqiang; Zhu, Yuanguo; Lu, Qinyun
2021
Diffusion on fractal objects modeling and its physics-informed neural network solution. Zbl 07465413
Zhao, Dazhi; Yu, Guozhu; Li, Weibin
2021
Variational principle and approximate solution for the fractal generalized Benjamin-Bona-Mahony-Burgers equation in fluid mechanics. Zbl 1482.35009
Wang, Kang-Jia; Wang, Guo-Dong
2021
Analytical solution of the fractal cubic-quintic Duffing equation. Zbl 1489.34002
Elías-Zúñiga, Alex; Palacios-Pineda, Luis Manuel; Jiménez-Cedeño, Isaac H.; Martínez-Romero, Oscar; Olvera-Trejo, Daniel
2021
Generalized synchronization and parameters identification of different-dimensional chaotic systems in the complex field. Zbl 1481.93061
Liu, Jian; Chen, Guanrong; Zhao, Xiu
2021
A novel perspective for the fractal Schrödinger equation. Zbl 1482.35011
Wang, Kang-Le
2021
Hermite-Hadamard type local fractional integral inequalities for generalized $$s$$-preinvex functions and their generalization. Zbl 1487.26055
Sun, Wenbing
2021
On the largest partial quotients in continued fraction expansions. Zbl 1483.11159
Fang, Lulu; Liu, Jian
2021
Solution of the local fractional generalized KdV equation using homotopy analysis method. Zbl 1482.35064
Jafari, Hossein; Prasad, Jyoti Geetesh; Goswami, Pranay; Dubey, Ravi Shanker
2021
Solvability of the Moore-Gibson-Thompson equation with viscoelastic memory term and integral condition via Galerkin method. Zbl 1482.35238
Boulaaras, Salah
2021
Low frequency property of a fractal vibration model for a concrete beam. Zbl 1482.74083
He, Chun-Hui; Liu, Chao; He, Ji-Huan; Gepreel, Khaled A.
2021
A new perspective on the study of the fractal coupled Boussinesq-Burger equation in shallow water. Zbl 07465643
Wang, Kang-Jia; Wang, Guo-Dong; Zhu, Hong-Wei
2021
Dynamical analysis of a novel discrete fractional SITRS model for COVID-19. Zbl 07542092
Elsonbaty, Amr; Sabir, Zulqurnain; Ramaswamy, Rajagopalan; Adel, Waleed
2021
An improvement of Hölder integral inequality on fractal sets and some related Simpson-like inequalities. Zbl 1481.26022
Luo, Chunyan; Yu, Yuping; Du, Tingsong
2021
An efficient ancient Chinese algorithm to investigate the dynamics response of a fractal microgravity forced oscillator. Zbl 1487.34095
Elías-Zúñiga, Alex; Martínez-Romero, Oscar; Olvera Trejo, Daniel; Palacios-Pineda, Luis Manuel
2021
A fractal model for effective thermal conductivity of dual-porosity media with randomly distributed tree-like networks. Zbl 1482.80006
Zhang, Jun; Wang, Yizhi; Lou, Gang; Kou, Jianlong
2021
Mild solutions of coupled hybrid fractional order system with Caputo-Hadamard derivatives. Zbl 07467695
Bedi, Pallavi; Kumar, Anoop; Abdeljawad, Thabet; Khan, Aziz; Gómez-Aguilar, J. F.
2021
Group analysis of the time fractional $$(3+1)$$-dimensional KdV-type equation. Zbl 1482.35025
Liu, Jian-Gen; Yang, Xiao-Jun; Geng, Lu-Lu; Fan, Yu-Rong
2021
On a generalization of strongly $$\eta$$-convex functions via fractal sets. Zbl 1487.26017
Robles, Zaroni; Sanabria, José E.; Sánchez C., Rainier V.
2021
Computational modeling and theoretical analysis of nonlinear fractional order prey-predator system. Zbl 1487.34099
Ali, Amjad; Shah, Kamal; Alrabaiah, Hussam; Shah, Zahir; Ur Rahman, Ghaus; Islam, Saeed
2021
A new stable internal structure of the Mandelbrot set during the iteration process. Zbl 1489.37064
Yu, Dakuan; Ta, Wurui
2021
Reliability index and option pricing formulas of the first-hitting time model based on the uncertain fractional-order differential equation with Caputo type. Zbl 1482.91204
Jin, Ting; Yang, Xiangfeng; Xia, Hongxuan; Ding, Hui
2021
Dynamics of fractional-order predator-prey model incorporating two delays. Zbl 1487.34162
Zhao, Lingzhi; Huang, Chengdai; Cao, Jinde
2021
Equivalent power-form transformation for fractal Bratu’s equation. Zbl 07465352
Elías-Zúñiga, Alex; Palacios-Pineda, Luis Manuel; Jiménez-Cedeño, Isaac H.; Martínez-Romero, Oscar; Olvera Trejo, Daniel
2021
What is the effect of the Weyl fractional integral on the Hölder continuous functions? Zbl 1486.26008
Cui, X. X.; Xiao, W.
2021
Application of optimized fractional grey model-based variable background value to predict electricity consumption. Zbl 1481.93097
Liu, Chong; Lao, Tongfei; Wu, Wen-Ze; Xie, Wanli
2021
Bifurcations emerging from different delays in a fractional-order predator-prey model. Zbl 1487.34160
Huang, Chengdai; Li, Huan; Chen, Xiaoping; Cao, Jinde
2021
A novel approach for fractal Burgers-BBM equation and its variational principle. Zbl 1482.35010
Wang, Kang-Le
2021
A new fractal transform frequency formulation for fractal nonlinear oscillators. Zbl 07465405
Wang, Kang-Le
2021
Image encryption technology based on fractional two-dimensional discrete chaotic map accompanied with Menezes-Vanstone elliptic curve cryptosystem. Zbl 1486.94126
Liu, Ze-Yu; Xia, Tiecheng; Wang, Yi-Ping
2021
The calculus of bivariate fractal interpolation surfaces. Zbl 1486.28006
Chandra, Subhash; Abbas, Syed
2021
Fractal analysis of shale gas transport through micropores and microfractures. Zbl 07465410
Gao, Qi; Cheng, Yuanfang; Han, Songcai; Li, Yang; Yan, Chuanliang; Han, Zhongying
2021
Dynamics of a fractional-order Bam neural network with leakage delay and communication delay. Zbl 1487.34152
Huang, Chengdai; Liu, Heng; Chen, Yuefen; Chen, Xiaoping; Song, Fang
2021
Stress sensitivity analysis of fractal porous media based on the elasto-plastic thick-walled cylinder model. Zbl 1482.74069
Huang, Zhaoqin; Su, Xin; Li, Yanchao; Zhang, Kai; Yao, Jun
2021
Finite-time stability in mean for nabla uncertain fractional order linear difference systems. Zbl 1481.39007
Lu, Qinyun; Zhu, Yuanguo; Li, Bo
2021
Assouad dimensions of Moran sets with zero infimum contraction. Zbl 1487.28006
Zhu, Zhiyong
2021
Existence results for ABC-fractional differential equations with non-separated and integral type of boundary conditions. Zbl 1487.34030
Mehmood, Nayyar; Abbas, Ahsan; Abdeljawad, Thabet; Akgül, Ali
2021
Monotonicity and asymptotic properties of solutions for parabolic equations via a given initial value condition on graphs. Zbl 1482.35058
Wu, Yiting
2021
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### Cited by 3,607 Authors

 44 Chand, Arya Kumar Bedabrata 36 Navascués, María Antonia 34 Xi, Lifeng 28 Viswanathan, Puthan Veedu 27 Su, Weiyi 26 Băleanu, Dumitru I. 23 Wang, Xingyuan 18 Dai, Meifeng 17 Strichartz, Robert S. 17 Vijender, Nallapu 16 Taqqu, Murad S. 15 Yao, Kui 13 Golmankhaneh, Alireza Khalili 12 El-Nabulsi, Rami Ahmad 12 Liang, Yongshun 12 Liu, Fawang 12 Wang, Qin 11 Karaca, Yeliz 11 Rashid, Saima 11 Rochon, Dominic 11 Selmi, Bilel 11 Yu, Boming 10 Bárány, Balázs 10 Chu, Yuming 10 Fraser, Jonathan MacDonald 10 Loridant, Benoit 10 Ma, Chunsheng 10 Ngai, Sze-Man 10 Teplyaev, Alexander 10 Xiao, Boqi 10 Xue, Yumei 10 Ye, Qianqian 9 Didier, Gustavo 9 Drakopoulos, Vasileios 9 Fan, Jiaqi 9 Khan, Ilyas 9 Leonenko, Nikolai N. 9 Thuswaldner, Jörg Maximilian 9 Yang, Xiao-Jun 8 Abdeljawad, Thabet 8 Anh, Vo V. 8 Bardet, Jean-Marc 8 Bouboulis, Pantelis 8 Dalla, Leoni 8 Gorenflo, Rudolf 8 Jiang, Kan 8 Jørgensen, Palle E. T. 8 Ju, Tingting 8 Katiyar, Saurabh Kumar 8 Lévy Véhel, Jacques 8 Machado, José António Tenreiro 8 Mainardi, Francesco 8 Meerschaert, Mark Marvin 8 Rezapour, Shahram 8 Ri, Songil 8 Stanley, H. Eugene 8 Sun, Yu 8 Telesca, Luciano 8 Turner, Ian William 8 Yun, Cholhui 7 Arneodo, Alain 7 Balankin, Alexander S. 7 Bory Reyes, Juan 7 Boulaaras, Salah Mahmoud 7 Falconer, Kenneth J. 7 Hilfer, Rudolf 7 Kovchegov, Yevgeniy V. 7 Long, Gongbo 7 Luo, Jun 7 Ma, Ying 7 Montoya, Fausto 7 Pastor, Gerardo 7 Prasad, M. Guru Prem 7 Romera, Miguel 7 Ruan, Huo-Jun 7 Sabir, Zulqurnain 7 Sandev, Trifce 7 Stenflo, Orjan 7 Wu, Bo 6 Abdo, Mohammed Salem 6 Ben Slimane, Mourad 6 Chen, Chen 6 Etemad, Sina 6 Gu, Jiangwen 6 Käenmäki, Antti 6 Li, Changpin 6 Li, Ming 6 Li, Wenxia 6 Li, Yin 6 Liu, Shutang 6 Luor, Dahchin 6 Miculescu, Radu 6 Morris, Ian D. 6 Prasad, Srijanani Anurag 6 Qiu, Hua 6 Rams, Michał 6 Saxena, Ram Kishore 6 Sebastián, María Victoria 6 Shahverdian, Ashot Yu. 6 Simon, Károly ...and 3,507 more Authors
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### Cited in 422 Journals

 461 Fractals 122 Chaos, Solitons and Fractals 88 Physica A 54 Journal of Mathematical Analysis and Applications 45 Applied Mathematics and Computation 37 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 36 Advances in Difference Equations 29 Chaos 29 Communications in Nonlinear Science and Numerical Simulation 28 Journal of Statistical Physics 28 Nonlinear Dynamics 25 Fractional Calculus & Applied Analysis 24 Computers & Mathematics with Applications 21 AIMS Mathematics 20 International Journal of Applied and Computational Mathematics 19 Journal of Mathematical Physics 19 Journal of Computational and Applied Mathematics 19 Physica D 18 Computational and Applied Mathematics 18 Mathematical Problems in Engineering 18 Journal of Statistical Mechanics: Theory and Experiment 16 International Journal of Computer Mathematics 16 Abstract and Applied Analysis 15 Physics Letters. A 14 Stochastic Processes and their Applications 13 Statistics & Probability Letters 13 Discrete Dynamics in Nature and Society 13 Mediterranean Journal of Mathematics 11 Ergodic Theory and Dynamical Systems 11 Bernoulli 11 Journal of Applied Mathematics and Computing 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Results in Mathematics 10 Transactions of the American Mathematical Society 10 Advances in Applied Clifford Algebras 10 International Journal of Modern Physics C 10 Journal of Function Spaces 9 Journal of Computational Physics 9 Advances in Mathematics 9 Proceedings of the American Mathematical Society 9 Advances in Mathematical Physics 9 Journal of Mathematics 8 Applied Mathematics Letters 8 Journal of Statistical Computation and Simulation 8 Computational Statistics and Data Analysis 8 The Journal of Fourier Analysis and Applications 8 Journal of Fractal Geometry 7 International Journal of Heat and Mass Transfer 7 Mathematics and Computers in Simulation 7 Stochastic Analysis and Applications 7 Acta Applicandae Mathematicae 7 Applied Numerical Mathematics 7 Journal of Theoretical Probability 7 Mathematical and Computer Modelling 7 Applied Mathematical Modelling 7 Turkish Journal of Mathematics 7 Complexity 7 Entropy 7 The European Physical Journal B. Condensed Matter and Complex Systems 6 Acta Mechanica 6 Bulletin of the Australian Mathematical Society 6 Communications in Mathematical Physics 6 Nonlinearity 6 Journal of Multivariate Analysis 6 Mathematische Nachrichten 6 Monatshefte für Mathematik 6 Theoretical Computer Science 6 Numerical Algorithms 6 Applied Mathematics. Series B (English Edition) 6 Journal of Inequalities and Applications 6 Quantitative Finance 6 Boundary Value Problems 6 Journal of Theoretical Biology 5 International Journal of Modern Physics B 5 International Journal of Theoretical Physics 5 Journal of Fluid Mechanics 5 Mathematical Proceedings of the Cambridge Philosophical Society 5 Journal of Approximation Theory 5 Journal of Statistical Planning and Inference 5 Mathematische Zeitschrift 5 Journal of Time Series Analysis 5 Communications in Statistics. Simulation and Computation 5 Indagationes Mathematicae. New Series 5 Experimental Mathematics 5 International Journal of Theoretical and Applied Finance 5 Journal of Applied Statistics 5 Analysis in Theory and Applications 5 Complex Analysis and Operator Theory 5 International Journal of Biomathematics 5 GEM - International Journal on Geomathematics 5 Statistics and Computing 5 Mathematics 4 Advances in Applied Probability 4 Applicable Analysis 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Mathematical Biology 4 Mathematics of Computation 4 The Annals of Statistics 4 Calcolo 4 Demonstratio Mathematica ...and 322 more Journals
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### Cited in 61 Fields

 790 Measure and integration (28-XX) 352 Real functions (26-XX) 312 Dynamical systems and ergodic theory (37-XX) 286 Probability theory and stochastic processes (60-XX) 281 Partial differential equations (35-XX) 270 Numerical analysis (65-XX) 242 Ordinary differential equations (34-XX) 193 Statistics (62-XX) 174 Statistical mechanics, structure of matter (82-XX) 133 Biology and other natural sciences (92-XX) 109 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 107 Approximations and expansions (41-XX) 100 Fluid mechanics (76-XX) 91 Combinatorics (05-XX) 82 Computer science (68-XX) 81 Information and communication theory, circuits (94-XX) 79 Harmonic analysis on Euclidean spaces (42-XX) 73 Operator theory (47-XX) 65 Number theory (11-XX) 50 Mechanics of deformable solids (74-XX) 47 Special functions (33-XX) 45 Functions of a complex variable (30-XX) 45 Systems theory; control (93-XX) 44 Operations research, mathematical programming (90-XX) 42 General topology (54-XX) 42 Geophysics (86-XX) 39 Quantum theory (81-XX) 37 Functional analysis (46-XX) 30 Potential theory (31-XX) 30 Convex and discrete geometry (52-XX) 26 Integral transforms, operational calculus (44-XX) 26 Integral equations (45-XX) 25 Calculus of variations and optimal control; optimization (49-XX) 24 Classical thermodynamics, heat transfer (80-XX) 23 Difference and functional equations (39-XX) 20 Global analysis, analysis on manifolds (58-XX) 20 Mechanics of particles and systems (70-XX) 15 Relativity and gravitational theory (83-XX) 14 Optics, electromagnetic theory (78-XX) 13 Differential geometry (53-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Geometry (51-XX) 9 General and overarching topics; collections (00-XX) 7 Mathematical logic and foundations (03-XX) 7 Group theory and generalizations (20-XX) 7 Topological groups, Lie groups (22-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Abstract harmonic analysis (43-XX) 6 Astronomy and astrophysics (85-XX) 6 Mathematics education (97-XX) 4 History and biography (01-XX) 4 Algebraic geometry (14-XX) 4 Algebraic topology (55-XX) 3 Commutative algebra (13-XX) 3 Category theory; homological algebra (18-XX) 3 Manifolds and cell complexes (57-XX) 2 Field theory and polynomials (12-XX) 2 Nonassociative rings and algebras (17-XX) 2 Sequences, series, summability (40-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX)