FractalsComplex 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 Comments: Journal; No longer indexed Documents Indexed: 1,689 Publications (1993–2023) References Indexed: 1,400 Publications with 41,605 References. all top 5 Latest Issues 31, No. 5 (2023) 31, No. 4 (2023) 31, No. 3 (2023) 31, No. 2 (2023) 31, No. 1 (2023) 30, No. 10 (2022) 30, No. 9 (2022) 30, No. 8 (2022) 30, No. 7 (2022) 30, No. 6 (2022) 30, No. 5 (2022) 30, No. 4 (2022) 30, No. 3 (2022) 30, No. 2 (2022) 30, No. 1 (2022) 29, No. 8 (2021) 29, No. 7 (2021) 29, No. 6 (2021) 29, No. 5 (2021) 29, No. 4 (2021) 29, No. 3 (2021) 29, No. 2 (2021) 29, No. 1 (2021) 28, No. 8 (2020) 28, No. 7 (2020) 28, No. 6 (2020) 28, No. 5 (2020) 28, No. 4 (2020) 28, No. 3 (2020) 28, No. 2 (2020) 28, No. 1 (2020) 27, No. 8 (2019) 27, No. 7 (2019) 27, No. 6 (2019) 27, No. 5 (2019) 27, No. 4 (2019) 27, No. 3 (2019) 27, No. 2 (2019) 27, No. 1 (2019) 26, No. 6 (2018) 26, No. 5 (2018) 26, No. 4 (2018) 26, No. 3 (2018) 26, No. 2 (2018) 26, No. 1 (2018) 25, No. 6 (2017) 25, No. 5 (2017) 25, No. 3 (2017) 25, No. 2 (2017) 25, No. 1 (2017) 24, No. 4 (2016) 24, No. 3 (2016) 24, No. 2 (2016) 24, No. 1 (2016) 23, No. 4 (2015) 23, No. 3 (2015) 23, No. 2 (2015) 22, No. 4 (2014) 22, No. 1-2 (2014) 21, No. 3-4 (2013) 21, No. 2 (2013) 21, No. 1 (2013) 20, No. 3-4 (2012) 20, No. 2 (2012) 20, No. 1 (2012) 19, No. 4 (2011) 19, No. 3 (2011) 19, No. 2 (2011) 19, No. 1 (2011) 18, No. 4 (2010) 18, No. 3 (2010) 18, No. 2 (2010) 18, No. 1 (2010) 17, No. 4 (2009) 17, No. 3 (2009) 17, No. 2 (2009) 17, No. 1 (2009) 16, No. 4 (2008) 16, No. 3 (2008) 16, No. 2 (2008) 16, No. 1 (2008) 15, No. 4 (2007) 15, No. 3 (2007) 15, No. 2 (2007) 15, No. 1 (2007) 14, No. 4 (2006) 14, No. 3 (2006) 14, No. 2 (2006) 14, No. 1 (2006) 13, No. 4 (2005) 13, No. 3 (2005) 13, No. 2 (2005) 13, No. 1 (2005) 12, No. 4 (2004) 12, No. 3 (2004) 12, No. 2 (2004) 12, No. 1 (2004) 11, No. 4 (2003) 11, No. 3 (2003) 11, No. 2 (2003) ...and 42 more Volumes all top 5 Authors 36 Abdeljawad, Thabet 34 Xi, Lifeng 26 Băleanu, Dumitru I. 25 Shah, Kamal 25 Wang, Kangle 21 Karaca, Yeliz 20 Chu, Yuming 20 Yu, Boming 19 Sooppy Nisar, Kottakkaran 19 Wang, Kang-Jia 17 Khan, Ilyas 17 Xiao, Boqi 14 Chand, Arya Kumar Bedabrata 14 Gómez-Aguilar, José Francisco 13 Dai, Meifeng 13 Rashid, Saima 13 Wang, Xingyuan 12 Khan, Aziz Ullah 12 Long, Gongbo 12 Su, Weiyi 11 Jafari, Hossein 11 Liang, Yongshun 11 Taqqu, Murad S. 11 Wang, Qin 11 Wu, Min 10 Akgül, Ali 10 Havlin, Shlomo 10 Navascués, María Antonia 10 Sabir, Zulqurnain 10 Wang, Guodong 10 Yao, Kui 9 Boulaaras, Salah Mahmoud 9 Elías-Zúñiga, Alex 9 Giona, Massimiliano 9 Jarad, Fahd 9 Raja, Muhammad Asif Zahoor 9 Riaz, Muhammad Bilal 9 Saeed, Tareq 9 Stanley, H. Eugene 9 ur Rahman, Mati 9 Xue, Yumei 9 Yao, Shaowen 9 Zeb, Anwar 8 Abdel-Aty, Abdel-Haleem 8 Amin, Rohul 8 Arfan, Muhammad 8 Atangana, Abdon 8 Bory Reyes, Juan 8 Du, Tingsong 8 He, Chun-Hui 8 Inc, Mustafa 8 Martínez-Romero, Oscar 8 Momani, Shaher M. 8 Olvera Trejo, Daniel 8 Palacios-Pineda, Luis Manuel 8 Shi, Feng 8 Strichartz, Robert S. 8 Takayasu, Hideki 8 Veneziano, Daniele 7 Ahmad, Hijaz 7 Alqudah, Manar A. 7 Alrabaiah, Hussam 7 Frame, Michael Lee 7 Huang, Chengdai 7 Jahanshahi, Hadi 7 Khalid, Aasma 7 Kumar, Sunil 7 Li, Wenxia 6 Agarwal, Praveen 6 Ahmad, Shabir 6 Brown, Christopher A. 6 Fan, Jiaqi 6 Hammouch, Zakia 6 Herrmann, Hans Jürgen 6 Jia, Qi 6 Jiang, Kan 6 Khan, Hasib 6 Khater, Mostafa M. A. 6 Kumam, Poom 6 Lei, Lei 6 Liu, Jiangen 6 Ma, Ying 6 Rochon, Dominic 6 Salahshour, Soheil 6 Shah, Zahir 6 Wang, Bo 6 Wang, Xiaoqian 6 Yang, Jiaojiao 6 Ye, Qianqian 6 Yusuf, Abdullahi A. 6 Zeng, Cheng 5 Abdalla, Mohamed 5 Ahmadian, Ali 5 Alassafi, Madini Obad 5 Alshomrani, Ali Saleh 5 Alzaid, Sara Salem 5 Buldyrev, Sergey V. 5 Cao, Jinde 5 Chauhan, Ram P. 5 Chen, Aimin ...and 2,750 more Authors all top 5 Fields 743 Measure and integration (28-XX) 266 Real functions (26-XX) 203 Ordinary differential equations (34-XX) 200 Dynamical systems and ergodic theory (37-XX) 191 Partial differential equations (35-XX) 182 Biology and other natural sciences (92-XX) 173 Numerical analysis (65-XX) 130 Probability theory and stochastic processes (60-XX) 129 Fluid mechanics (76-XX) 99 Computer science (68-XX) 95 Statistical mechanics, structure of matter (82-XX) 72 Combinatorics (05-XX) 64 Information and communication theory, circuits (94-XX) 60 Statistics (62-XX) 56 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 52 Mechanics of deformable solids (74-XX) 49 Geophysics (86-XX) 47 Operator theory (47-XX) 42 Number theory (11-XX) 40 Systems theory; control (93-XX) 34 Harmonic analysis on Euclidean spaces (42-XX) 33 Approximations and expansions (41-XX) 31 General and overarching topics; collections (00-XX) 30 Operations research, mathematical programming (90-XX) 27 Classical thermodynamics, heat transfer (80-XX) 26 Optics, electromagnetic theory (78-XX) 22 Difference and functional equations (39-XX) 21 Integral equations (45-XX) 18 Mechanics of particles and systems (70-XX) 15 Functions of a complex variable (30-XX) 15 Special functions (33-XX) 14 Integral transforms, operational calculus (44-XX) 13 Quantum theory (81-XX) 12 Global analysis, analysis on manifolds (58-XX) 11 Calculus of variations and optimal control; optimization (49-XX) 9 Convex and discrete geometry (52-XX) 9 General topology (54-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Functional analysis (46-XX) 5 Astronomy and astrophysics (85-XX) 3 Mathematical logic and foundations (03-XX) 3 Nonassociative rings and algebras (17-XX) 3 Potential theory (31-XX) 3 Sequences, series, summability (40-XX) 3 Geometry (51-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Abstract harmonic analysis (43-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 988 Publications have been cited 5,570 times in 3,352 Documents Cited by ▼ Year ▼ Estimators for long-range dependence: An empirical study. Zbl 0864.62061 Taqqu, Murad S.; Teverovsky, Vadim; Willinger, Walter 99 1995 The relationship between fractional calculus and fractals. Zbl 0877.28009 Tatom, Frank B. 98 1995 Distributed order fractional sub-diffusion. Zbl 1083.60066 Naber, Mark 81 2004 Bivariate fractal interpolation functions on grids. Zbl 1088.28502 Dalla, Leoni 54 2002 Calculus on fractal subsets of real line. I: Formulation. Zbl 1173.28005 Parvate, Abhay; Gangal, A. D. 49 2009 The study of bivariate fractal interpolation functions and creation of fractal interpolated surfaces. Zbl 0908.65005 Xie, Heping; Sun, Hongquan 48 1997 Average geodesic distance of Sierpinski gasket and Sierpinski networks. Zbl 1375.28020 Wang, Songjing; Yu, Zhouyu; Xi, Lifeng 46 2017 Hidden variable bivariate fractal interpolation surfaces. Zbl 1046.28004 Chand, A. K. B.; Kapoor, G. P. 44 2003 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 41 2017 On the Riemann-Liouville fractional calculus and some recent applications. Zbl 0868.26004 Nonnenmacher, Theo F.; Metzler, Ralf 38 1995 On Hadamard fractional calculus. Zbl 1371.26009 Ma, Li; Li, Changpin 37 2017 Certain integral inequalities considering generalized \(m\)-convexity on fractal sets and their applications. Zbl 1434.28018 Du, Tingsong; Wang, Hao; Khan, Muhammad Adil; Zhang, Yao 37 2019 A generalized Mandelbrot set for bicomplex numbers. Zbl 0969.37021 Rochon, Dominic 35 2000 Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform. Zbl 1083.65005 Stoev, Stilian; Taqqu, Murad S. 35 2004 Cooperative strategies in formation of complex bacterial patterns. Zbl 0869.92002 Ben-Jacob, Eshel; Shochet, Ofer; Cohen, Inon; Tenenbaum, Adam; Czirók, Andras; Vicsek, Tamas 35 1995 On fractional relaxation. Zbl 1140.82315 Hilfer, R. 34 2003 Fractal bases of \(L_p\) spaces. Zbl 1251.28009 Navascués, M. A. 34 2012 Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302 Falconer, Kenneth; Miao, Jun 31 2007 On the weighted fractional operators of a function with respect to another function. Zbl 1489.26006 Jarad, F.; Abdeljawad, T.; Shah, K. 31 2020 Hidden variable vector valued fractal interpolation functions. Zbl 1100.41011 Bouboulis, P.; Dalla, L. 30 2005 A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004 Barnsley, Michael; Hutchinson, John; Stenflo, Örjan 30 2005 Multifractal cascade dynamics and turbulent intermittency. Zbl 0927.76044 Schertzer, D.; Lovejoy, S.; Schmitt, F.; Chigirinskaya, Y.; Marsan, D. 29 1997 Topological structure of self-similar sets. Zbl 1075.28005 Luo, Jun; Rao, Hui; Tan, Bo 29 2002 Some further extensions considering discrete proportional fractional operators. Zbl 1495.26021 Rashid, Saima; Sultana, Sobia; Karaca, Yeliz; Khalid, Aasma; Chu, Yu-Ming 29 2022 Analysis of fractional differential equations with multi-orders. Zbl 1176.34008 Deng, Weihua; Li, Changpin; Guo, Qian 28 2007 Average geodesic distance of Sierpinski carpet. Zbl 1432.28015 Zhao, Luming; Wang, Songjing; Xi, Lifeng 27 2017 Calculus on fractal subsets of real line. II: Conjugacy with ordinary calculus. Zbl 1252.28005 Parvate, Abhay; Gangal, A. D. 26 2011 The reproducing kernel algorithm for numerical solution of Van der Pol damping model in view of the Atangana-Baleanu fractional approach. Zbl 07468592 Momani, Shaher; Maayah, Banan; Arqub, Omar Abu 26 2020 On the dimension of self-similar sets. Zbl 1088.28504 Simon, Károly; Solomyak, Boris 25 2002 Box dimensions of {\(\alpha\)}-fractal functions. Zbl 1354.28002 Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A. 25 2016 Piecewise optimal fractional reproducing kernel solution and convergence analysis for the Atangana-Baleanu-Caputo model of the Lienard’s equation. Zbl 07468589 Momani, Shaher; Arqub, Omar Abu; Maayah, Banan 25 2020 Calculus on fractal curves in \(\mathbb{R}^{n}\). Zbl 1217.28014 Parvate, Abhay; Satin, Seema; Gangal, A. D. 24 2011 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. 24 2008 Numerical solution of traveling waves in chemical kinetics: time-fractional fishers equations. Zbl 07507535 Wang, Fuzhang; Khan, Muhammad Nawaz; Ahmad, Imtiaz; Ahmad, Hijaz; Abu-Zinadah, Hanaa; Chu, Yu-Ming 24 2022 Exact solutions for a class of fractal time random walks. Zbl 0881.60066 Hilfer, R. 23 1995 Analysis of fractal-fractional malaria transmission model. Zbl 1482.92097 Gómez-Aguilar, J. F.; Córdova-Fraga, T.; Abdeljawad, Thabet; Khan, Aziz; Khan, Hasib 23 2020 Newton’s-type integral inequalities via local fractional integrals. Zbl 1434.26052 Iftikhar, Sabah; Kumam, Poom; Erden, Samet 22 2020 Foundations of fractional dynamics. Zbl 0870.58041 Hilfer, R. 21 1995 Dimension analysis of continuous functions with unbounded variation. Zbl 1371.28012 Wang, Jun; Yao, Kui 21 2017 The multifractal dimension functions of homogeneous Moran measure. Zbl 1165.28005 Xiao, Jiaqing; Wu, Min 20 2008 Modifications at large distances from fractional and fractal arguments. Zbl 1196.28014 El-Nabulsi, Rami Ahmad 20 2010 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 19 2000 Normal families of bicomplex holomorphic functions. Zbl 1230.30032 Charak, K. S.; Rochon, D.; Sharma, N. 19 2009 Nonextensive thermostatics and fractals. Zbl 0870.58098 Tsallis, Constantino 19 1995 Path properties of the linear multifractional stable motion. Zbl 1304.28010 Stoev, Stilian; Taqqu, Murad S. 19 2005 Average distance of self-similar fractal trees. Zbl 1432.28007 Li, Tingting; Jiang, Kan; Xi, Lifeng 19 2018 \(1/f\) noise in a traffic model. Zbl 0906.90072 Takayasu, Misako; Takayasu, Hideki 18 1993 Fractal image compression. Zbl 0903.68211 Fisher, Yuval 18 1994 Spectral analysis for weighted iterated triangulations of graphs. Zbl 1432.35058 Chen, Yufei; Dai, Meifeng; Wang, Xiaoqian; Sun, Yu; Su, Weiyi 18 2018 The Hosoya index of graphs formed by a fractal graph. Zbl 1434.05039 Liu, Jia-bao; Zhao, Jing; Min, Jie; Cao, Jinde 18 2019 Variational principle and approximate solution for the generalized Burgers-Huxley equation with fractal derivative. Zbl 1482.35008 Wang, Kang-Jia 18 2021 Two-scale fractal theory for the population dynamics. Zbl 1481.92098 Anjum, Naveed; He, Chun-Hui; He, Ji-Huan 18 2021 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. 17 2007 Fractal geometry of financial time series. Zbl 0869.62073 Evertsz, Carl J. G. 17 1995 A type of fractal interpolation functions and their fractional calculus. Zbl 1351.28016 Liang, Yong-Shun; Zhang, Qi 17 2016 A technique in the topology of connected self-similar tiles. Zbl 1304.28009 Ngai, Sze-Man; Tang, Tai-Man 17 2004 A new perspective to study the third-order modified KdV equation on fractal set. Zbl 1445.28012 Liu, Jian-Gen; Yang, Xiao-Jun; Feng, Yi-Ying; Cui, Ping 17 2020 Numerical solution of distributed order integro-differential equations. Zbl 1505.65324 Zhang, Anqi; Ganji, Roghayeh Moallem; Jafari, Hossein; Ncube, Mahluli Naisbitt; Agamalieva, Latifa 17 2022 A new nonlinear fractal interpolation function. Zbl 1432.41001 Ri, Songil 17 2017 Eccentric distance sum of Sierpiński gasket and Sierpiński network. Zbl 1433.28009 Chen, Jin; He, Long; Wang, Qin 17 2019 A remark on Wang’s fractal variational principle. Zbl 1434.35267 Wang, Kang-Le; He, Chun-Hui 17 2019 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. 17 2021 Explicit construction of operator scaling Gaussian random fields. Zbl 1233.60027 Clausel, M.; Vedel, B. 16 2011 On a generalized Fatou-Julia theorem in multicomplex spaces. Zbl 1177.30068 Garant-Pelletier, V.; Rochon, D. 16 2009 Some local fractional integral inequalities for generalized preinvex functions and applications to numerical quadrature. Zbl 1434.26015 Sun, Wenbing 16 2019 Fractal modeling of speech signals. Zbl 1126.94308 Lévy Véhel, Jacques; Daoudi, Khalid; Lutton, Evelyne 15 1994 Analysis on fractals in fuzzy metric spaces. Zbl 1231.26030 Easwaramoorthy, D.; Uthayakumar, R. 15 2011 An analysis of U.S. stock price behavior using wavelets. Zbl 0877.90027 Ramsey, James B.; Usikov, Daniel; Zaslavsky, George M. 15 1995 Estimation and simulation of fractal stochastic point processes. Zbl 0881.60044 Lowen, Steven B.; Teich, Malvin C. 15 1995 Construction and analysis of a special one-dimensional continuous function. Zbl 1371.28011 Wang, J.; Yao, Kui 15 2017 Cantor-type sets in hyperbolic numbers. Zbl 1357.28008 Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M. 15 2016 Asymptotic formula of eccentric distance sum for Vicsek network. Zbl 1433.28036 Ye, Qianqian; He, Long; Wang, Qin; Xi, Lifeng 15 2018 Progress on estimation of fractal dimensions of fractional calculus of continuous functions. Zbl 1434.26010 Liang, Yong-Shun 15 2019 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 15 2018 Lipschitz equivalence of McMullen sets. Zbl 1290.28012 Li, Boming; Li, Wenxia; Miao, Jun Jie 15 2013 A fractal-Monte Carlo approach to model oil and water two-phase seepage in low-permeability reservoirs with rough surfaces. Zbl 1500.76088 Su, Haibo; Zhang, Yidan; Xiao, Boqi; Huang, Xiaoming; Yu, Boming 15 2021 A fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media. Zbl 1500.76091 Xiao, Boqi; Huang, Qiwen; Chen, Hanxin; Chen, Xubing; Long, Gongbo 15 2021 Analysis of mixed Weyl-Marchaud fractional derivative and box dimensions. Zbl 1491.28003 Chandra, Subhash; Abbas, Syed 15 2021 Existence results and stability criteria for ABC-fuzzy-Volterra integro-differential equation. Zbl 1482.45005 Khan, Hasib; Gomez-Aguilar, J. F.; Abdeljawad, Thabet; Khan, Aziz 15 2020 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. 14 1997 On stability of fractal interpolation. Zbl 0974.28003 Feng, Zhigang; Xie, Heping 14 1998 On a generalized Fatou-Julia theorem. Zbl 1041.37023 Rochon, Dominic 14 2003 Fractal trigonometric polynomials for restricted range approximation. Zbl 1351.28009 Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K. 14 2016 Fractal interpolation functions on post critically finite self-similar sets. Zbl 1196.28019 Ruan, Huo-Jun 14 2010 The average weighted path length for a class of hierarchical networks. Zbl 1441.05208 Niu, Min; Li, Ruixia 14 2020 Natural cubic spline coalescence hidden variable fractal interpolation surfaces. Zbl 1250.28004 Chand, A. K. B. 14 2012 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 14 2022 The calculus of bivariate fractal interpolation surfaces. Zbl 1486.28006 Chandra, Subhash; Abbas, Syed 14 2021 A fractal model for predicting oxygen effective diffusivity of porous media with rough surfaces under dry and wet conditions. Zbl 1500.76079 Xiao, Boqi; Huang, Qiwen; Yu, Boming; Long, Gongbo; Chen, Hanxin 14 2021 Symmetry analysis, analytical solutions and conservation laws of a generalized KdV-Burgers-Kuramoto equation and its fractional version. Zbl 1482.35027 Wang, Gangwei 14 2021 An user intention mining model based on fractal time series pattern. Zbl 1508.68316 Wu, Shaofei 14 2020 Approximate endpoint solutions for a class of fractional \(q\)-differential inclusions by computational results. Zbl 07468611 Aydogan, S. M.; Aguilar, J. F. Gómez; Baleanu, D.; Rezapour, Sh.; Samei, M. E. 14 2020 Image compression using affine fractal interpolation on rectangular lattices. Zbl 1158.68051 Drakopoulos, V.; Bouboulis, P.; Theodoridis, S. 13 2006 Definition, properties and wavelet analysis of multiscale fractional Brownian motion. Zbl 1142.60329 Bardet, Jean-Marc; Bertrand, Pierre 13 2007 On the Assouad dimension of graph directed Moran fractals. Zbl 1222.28017 Olsen, L. 13 2011 Green’s functions on fractals. Zbl 0983.31005 Kigami, Jun; Sheldon, Daniel R.; Strichartz, Robert S. 13 2000 On smoothness for a class of fractal interpolation surfaces. Zbl 1302.37020 Wang, Hong-Yong 13 2006 Information volume fractal dimension. Zbl 1491.94029 Gao, Qiuya; Wen, Tao; Deng, Yong 13 2021 Asymptotic formula of average distances on fractal networks modeled by Sierpinski tetrahedron. Zbl 1434.28017 Deng, Juan; Wang, Qin 13 2019 Novel approach for fractal nonlinear oscillators with discontinuities by Fourier series. Zbl 1502.34026 Wang, Kang-Le 13 2022 On fractal-fractional waterborne disease model: a study on theoretical and numerical aspects of solutions via simulations. Zbl 1520.92068 Khan, Hasib; Alzabut, Jehad; Shah, Anwar; He, Zai-Yin; Etemad, Sina; Rezapour, Shahram; Zada, Akbar 3 2023 New fractal soliton solutions for the coupled fractional Klein-Gordon equation with \(\beta\)-fractional derivative. Zbl 1518.35651 Wang, Kangle 3 2023 Construction of fractal soliton solutions for the fractional evolution equations with conformable derivative. Zbl 1521.35162 Wang, Kangle 3 2023 \(n\)-soliton, breather, lump solutions and diverse traveling wave solutions of the fractional \((2+1)\)-Dimensional Boussinesq equation. Zbl 1521.35142 Wang, Kang-Jia; Liu, Jing-Hua; Si, Jing; Shi, Feng; Wang, Guo-Dong 3 2023 A novel numerical method for solving fuzzy variable-order differential equations with Mittag-Leffler kernels. 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Zbl 1521.35193 Tuan, Nguyen Huy; Nguyen, Van Tien; O’Regan, Donal; Can, Nguyen Huu; Nguyen, Van Thinh 1 2023 Epidemiological analysis of human liver model with fractional operator. Zbl 07726750 Azeem, Muhammad; Farman, Muhammad; Abukhaled, Marwan; Nisar, Kottakkaran Sooppy; Akgül, Ali 1 2023 Analysis of the conformable temporal-fractional Swift-Hohenberg equation using a novel computational technique. Zbl 07726753 Khan, Aziz; Liaqat, Muhammad Imran; Alqudah, Manar A.; Abdeljawad, Thabet 1 2023 Application of Hosoya polynomial to solve a class of time-fractional diffusion equations. Zbl 1521.35187 Jafari, Hossein; Ganji, Roghayeh Moallem; Narsale, Sonali Mandar; Kgarose, Maluti; Nguyen, Van Thinh 1 2023 Semi-analytical view of time-fractional PDEs with proportional delays pertaining to index and Mittag-Leffler memory interacting with hybrid transforms. Zbl 1522.35563 Shi, Lei; Rashid, Saima; Sultana, Sobia; Khalid, Aasma; Agarwal, Praveen; Osman, Mohamed S. 1 2023 Variational principle and solitary wave of the fractal fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave model. Zbl 07726779 Sun, Jianshe 1 2023 The Simpson-type integral inequalities involving twice local fractional differentiable generalized \((s, P)\)-convexity and their applications. Zbl 07726781 Zhou, Yunxiu; Du, Tingsong 1 2023 A new fractal modified Benjamin-Bona-Mahony equation: its generalized variational principle and abundant exact solutions. Zbl 07726790 Wang, Kang-Jia; Si, Jing; Wang, Guo Dong; Shi, Feng 1 2023 Spectral analysis for weighted level-4 Sierpiński graphs and its applications. Zbl 1519.05110 Zhu, Xingchao; Zhu, Zhiyong 1 2023 Investigation of financial bubble mathematical model under fractal-fractional Caputo derivative. Zbl 1521.91346 Li, Bo; Zhang, Tongxin; Zhang, Chao 1 2023 Local geometry of self-similar sets: typical balls, tangent measures and asymptotic spectra. Zbl 07726801 Morán, Manuel; Llorente, Marta; Mera, María Eugenia 1 2023 Stress-dependent models for permeability and porosity of fractured rock based on fractal theory. Zbl 07726806 Miao, Tongjun; Chen, Aimin; Li, Zun; Liu, Daping; Yu, Boming 1 2023 Existence results for multi-term fractional differential equations with nonlocal boundary conditions involving Atangana-Baleanu derivative. Zbl 07700472 Abbas, Ahsan; Mehmood, Nayyar; Akgül, Ali; Abdeljawad, Thabet; Alqudah, Manar A. 1 2023 Adapted homotopy perturbation method with Shehu transform for solving conformable fractional nonlinear partial differential equations. Zbl 1518.35634 Liaqat, Muhammad Imran; Khan, Aziz; Alqudah, Manar A.; Abdeljawad, Thabet 1 2023 Characterizations of the inversion formula of the continuous Bessel wavelet transform of distributions in \(H_\mu^\prime(\mathbb{R}^+)\). Zbl 1527.46027 Maurya, Jay Singh; Upadhyay, Santosh Kumar 1 2023 Simpson-like inequalities for twice differentiable \((s, P)\)-convex mappings involving with AB-fractional integrals and their applications. Zbl 07700490 Yuan, Xiaoman; Xu, Lei; Du, Tingsong 1 2023 Non-differentiable exact solutions of the local fractional Zakharov-Kuznetsov equation on the Cantor sets. Zbl 07700494 Wang, Kang-Jia; Shi, Feng; Si, Jing; Liu, Jing-Hua; Wang, Guo-Dong 1 2023 Totally new soliton phenomena in the fractional Zoomeron model for shallow water. Zbl 1521.35164 Wang, Kang-Le 1 2023 Some further extensions considering discrete proportional fractional operators. Zbl 1495.26021 Rashid, Saima; Sultana, Sobia; Karaca, Yeliz; Khalid, Aasma; Chu, Yu-Ming 29 2022 Numerical solution of traveling waves in chemical kinetics: time-fractional fishers equations. Zbl 07507535 Wang, Fuzhang; Khan, Muhammad Nawaz; Ahmad, Imtiaz; Ahmad, Hijaz; Abu-Zinadah, Hanaa; Chu, Yu-Ming 24 2022 Numerical solution of distributed order integro-differential equations. Zbl 1505.65324 Zhang, Anqi; Ganji, Roghayeh Moallem; Jafari, Hossein; Ncube, Mahluli Naisbitt; Agamalieva, Latifa 17 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 14 2022 Novel approach for fractal nonlinear oscillators with discontinuities by Fourier series. Zbl 1502.34026 Wang, Kang-Le 13 2022 Fractal variational principles for two different types of fractal plasma models with variable coefficients. Zbl 1493.35133 Wang, Kang-Le; Wang, Hao 10 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 10 2022 Parameter-varying artificial potential field control of virtual coupling system with nonlinear dynamics. Zbl 1485.93023 Cao, Yuan; Wen, Jiakun; Hobiny, Aatef; Li, Peng; Wen, Tao 10 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 10 2022 Fractal solitary wave solutions for fractal nonlinear dispersive Boussinesq-like models. Zbl 1504.35390 Wang, Kangle 9 2022 A novel perspective to the local fractional bidirectional wave model on Cantor sets. Zbl 1502.78013 Wang, Kangle 8 2022 Information fractal dimension of mass function. Zbl 1512.28003 Qiang, Chenhui; Deng, Yong; Cheong, Kang Hao 8 2022 Abundant exact traveling wave solutions to the local fractional \((3+1)\)-dimensional Boiti-Leon-Manna-Pempinelli equation. Zbl 1491.35106 Wang, Kang-Jia; Wang, Guo-Dong; Shi, Feng 7 2022 Jensen-Mercer inequality and related results in the fractal sense with applications. Zbl 1495.26026 Butt, Saad Ihsan; Yousaf, Saba; Ahmad, Hijaz; Nofal, Taher A. 7 2022 Caputo type fractional operator applied to hepatitis B system. Zbl 1492.34051 Din, Anwarud; Li, Yongjin; Yusuf, Abdullahi; Ali, Aliyu Isa 7 2022 A modified frequency-amplitude formulation for fractal vibration systems. Zbl 1507.74163 He, Chun-Hui; Liu, Chao 6 2022 A novel permeability model in damaged tree-like bifurcating networks considering the influence of roughness. Zbl 1496.28008 Liu, Zhenjie; Gao, Jun; Xiao, Boqi; Cao, Jiyin; Fang, Jing; Liang, Mingchao; Long, Gongbo 6 2022 A fractal modification of the unsteady Korteweg-de Vries model and its generalized fractal variational principle and diverse exact solutions. Zbl 1509.35247 Wang, Kang-Jia 6 2022 Exact traveling wave solution for the fractal Riemann wave model Arising in ocean science. Zbl 1501.35118 Wang, Kangle 6 2022 Computational analysis of fractional order imperfect testing infection disease model. Zbl 1504.34114 Khan, Zareen A.; Khan, Aziz; Abdeljawad, Thabet; Khan, Hasib 5 2022 Exact traveling wave solutions for the local fractional Kadomtsov-Petviashvili-Benjamin-Bona-Mahony model by variational perspective. Zbl 1507.35333 Wang, Kangle 5 2022 Shifted Legendre fractional pseudospectral differentiation matrices for solving fractional differential problems. Zbl 07490674 Abdelhakem, Mohamed; Abdelhamied, Dina; Alshehri, Maryam G.; El-Kady, Mamdouh 5 2022 Existence results for a coupled system of nonlinear fractional \(q\)-integro-difference equations with \(q\)-integral-coupled boundary conditions. Zbl 1485.39008 Alsaedi, Ahmed; Al-Hutami, Hana; Ahmad, Bashir; Agarwal, Ravi P. 5 2022 Research on the nonlinear vibration of carbon nanotube embedded in fractal medium. Zbl 1496.74069 Wang, Kang-Jia 5 2022 Bäcklund transformation and diverse exact explicit solutions of the fractal combined KdV-mKdV equation. Zbl 1509.35270 Wang, Kang-Jia 5 2022 Analyses of some structural properties on a class of hierarchical scale-free networks. Zbl 1502.90033 Liu, Jia-Bao; Bao, Yan; Zheng, Wu-Ting 5 2022 Generalized variational principles and new abundant wave structures of the fractal coupled Boussinesq equation. Zbl 1501.35007 Wang, Kang-Jia; Wang, Guo-Dong; Shi, Feng; Zhu, Hong-Wei 5 2022 A novel variational approach to fractal Swift-Hohenberg model arising in fluid dynamics. Zbl 1501.35008 Wang, Kang-Le 5 2022 Fractal Hadamard-Mercer-type inequalities with applications. Zbl 1494.26037 Butt, Saad Ihsan; Yousaf, Saba; Younas, Muhammad; Ahmad, Hijaz; Yao, Shao-Wen 5 2022 An improvement of the power-mean integral inequality in the frame of fractal space and certain related midpoint-type integral inequalities. Zbl 1502.26028 Yu, Shuhong; Mohammed, Pshtiwan Othman; Xu, Lei; Du, Tingsong 5 2022 A fractal model of power-law fluid through charged fibrous porous media by using the fractional-derivative theory. Zbl 1494.76090 Xiao, Boqi; Li, Yupeng; Long, Gongbo 4 2022 Heat equations defined by self-similar measures with overlaps. Zbl 1491.35088 Tang, Wei; Ngai, Sze-Man 4 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 4 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 4 2022 The numerical strategy of tempered fractional derivative in European double barrier option. Zbl 1484.91521 Xie, Chengxuan; Xia, Xiaoxiao; Aghdam, Yones Esmaeelzade; Farnam, Behnaz; Jafari, Hossein; Wang, Shuchun 4 2022 Solitary waves of the fractal regularized long-wave equation traveling along an unsmooth boundary. Zbl 1507.35205 Wang, Kang-Jia; Li, Geng; Liu, Jing-Hua; Wang, Guo-Dong 4 2022 Dynamics of crime transmission using fractional-order differential equations. Zbl 1502.34054 Bansal, Komal; Arora, Sugandha; Pritam, Kocherlakota Satya; Mathur, Trilok; Agarwal, Shivi 4 2022 On the generalized weighted Caputo-type differential operator. Zbl 1495.26011 Liu, Jian-Gen; Yang, Xiao-Jun; Feng, Yi-Ying; Geng, Lu-Lu 4 2022 Periodic wave structure of the fractal generalized fourth-order Boussinesq equation traveling along the non-smooth boundary. Zbl 1509.35248 Wang, Kang-Jia; Shi, Feng; Wang, Guo-Dong 4 2022 Novel scheme for the fractal-fractional short water wave model with unsmooth boundaries. Zbl 1509.35250 Wang, Kangle 4 2022 Application of the extended f-expansion method for solving the fractional Gardner equation with conformable fractional derivative. Zbl 1501.35012 Wang, Kang-Jia; Shi, Feng; Liu, Jing-Hua; Si, Jing 4 2022 Hadamard fractional calculus on time scales. Zbl 1515.26032 Song, Ting-Ting; Wu, Guo-Cheng; Wei, Jia-Li 4 2022 Bounded variation on the Sierpiński gasket. Zbl 1522.28012 Verma, S.; Sahu, A. 4 2022 A new \((3+1)\)-Dimensional KdV equation and mkdv equation with their corresponding fractional forms. Zbl 1504.35456 Wang, Gangwei; Wazwaz, Abdul-Majid 4 2022 Gudermannian neural networks to investigate the Liénard differential model. Zbl 07537366 Wang, Bo; Wang, Ye; Gómez-Aguilar, J. F.; Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Jahanshahi, Hadi; Alassafi, Madini O.; Alsaadi, Fawaz E. 3 2022 Use of evolutionary algorithms in a fractional framework to prevent the spread of coronavirus. Zbl 1498.92267 Wang, Bo; Jahanshahi, Hadi; Karaca, Yeliz; Bekiros, Stelios; Xia, Wei-Feng; Alkhateeb, Abdulhameed F.; Nour, Majid 3 2022 Numerical computing to solve the nonlinear corneal system of eye surgery using the capability of morlet wavelet artificial neural networks. Zbl 07578007 Wang, Bo; Gómez-Aguilar, J. F.; Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Xia, Wei-Feng; Jahanshahi, Hadi; Alassafi, Madini O.; Alsaadi, Fawaz E. 3 2022 Computational study of fractional-order vector borne diseases model. Zbl 07578009 Bedi, Pallavi; Khan, Aziz; Kumar, Anoop; Abdeljawad, Thabet 3 2022 Modeling the dynamics of stochastic norovirus epidemic model with time delay. Zbl 1498.92270 Wang, Ye; Abdeljawad, Thabet; Din, Anwarud 3 2022 A hybrid approach for synchronizing between two reaction-diffusion systems of integer- and fractional-order applied on certain chemical models. Zbl 1498.93696 Wang, Bo; Ouannas, Adel; Karaca, Yeliz; Xia, Wei-Feng; Jahanshahi, Hadi; Alkhateeb, Abdulhameed F.; Nour, Majid 3 2022 Exact traveling wave solutions to the local fractional \((3+1)\)-dimensional Jimbo-Miwa equation on Cantor sets. Zbl 1501.35117 Wang, Kang-Jia 3 2022 Analysis of thermal conductivity of damaged tree-like bifurcation network with fractal roughened surfaces. Zbl 07610608 Xiao, Boqi; Fang, Jing; Long, Gongbo; Tao, Yuanzhang; Huang, Zijun 3 2022 Fractal permeability model for power-law fluids in fractured porous media with rough surfaces. Zbl 1506.76179 Xiao, Boqi; Li, Yupeng; Long, Gongbo; Yu, Boming 3 2022 New inequalities on generalized \(m\)-convexity on fractal sets. Zbl 1515.26028 Sánchez C., Rainier V.; Sanabria, José E.; Trousselot, Eduard 3 2022 A mixed multifractal analysis for quasi-Ahlfors vector-valued measures. Zbl 1495.28007 Ben Mabrouk, Anouar; Farhat, Adel 3 2022 Chaotic behavior of Bhalekar-Gejji dynamical system under Atangana-Baleanu fractal fractional operator. Zbl 1493.37091 Ahmad, Shabir; Ullah, Aman; Akgül, Ali; Abdeljawad, Thabet 3 2022 On the complex mixed dark-bright wave distributions to some conformable nonlinear integrable models. Zbl 1507.35233 Ciancio, Armando; Yel, Gulnur; Kumar, Ajay; Baskonus, Haci Mehmet; Ilhan, Esin 3 2022 Strange nonchaotic attractors in a periodically forced piecewise linear system with noise. Zbl 1493.37040 Li, Gaolei; Yue, Yuan; Grebogi, Celso; Li, Denghui; Xie, Jianhua 3 2022 A quaternionic fractional Borel-Pompeiu-type formula. Zbl 1486.30135 González-Cervantes, José Oscar; Bory-Reyes, Juan 3 2022 Existence results and numerical study on novel coronavirus 2019-nCoV/SARS-CoV-2 model using differential operators based on the generalized Mittag-Leffler kernel and fixed points. Zbl 1508.92289 Panda, Sumati Kumari; Atangana, Abdon; Abdeljawad, Thabet 3 2022 Analysis and implementation of numerical scheme for the variable-order fractional modified sub-diffusion equation. Zbl 1509.65068 Ali, Umair; Naeem, Muhammad; Abdullah, Farah Aini; Wang, Miao-Kun; Salama, Fouad Mohammad 3 2022 Dynamic response of a fractal cushioning packaging system. Zbl 1504.74064 Elías-Zúñiga, Alex; Palacios-Pineda, Luis Manuel; Olvera Trejo, Daniel; Martínez-Romero, Oscar 3 2022 On box dimension of Hadamard fractional integral (partly answer fractal calculus conjecture). Zbl 1508.28002 Xiao, Wei 3 2022 Reproducing kernel Hilbert spaces of functions for curve fitting problems. Zbl 1506.28008 Luor, Dah-Chin 2 2022 Hopf bifurcation of a fractional tri-neuron network with different orders and leakage delay. Zbl 1500.34060 Wang, Yangling; Cao, Jinde; Huang, Chengdai 2 2022 An insight on the fractal power law flow: from a Hausdorff vector calculus perspective. Zbl 1490.28005 Yang, Xiao-Jun 2 2022 On two-scale dimension and its application for deriving a new analytical solution for the fractal Duffing’s equation. Zbl 1506.70025 Elías-Zúñiga, Alex 2 2022 A nonlocal modeling for solving time fractional diffusion equation arising in fluid mechanics. Zbl 1497.65204 Hosseini, Vahid Reza; Rezazadeh, Arezou; Zheng, Hui; Zou, Wennan 2 2022 The numerical meshless approach for solving the 2D time nonlinear multi-term fractional cable equation in complex geometries. Zbl 1496.65134 Zou, Wennan; Tang, Yu; Hosseini, Vahid Reza 2 2022 Case study on total controllability and optimal control of Hilfer neutral non-instantaneous fractional derivative. Zbl 1504.34226 Sooppy Nisar, Kottakkaran; Ravichandran, C.; Abdel-Aty, Abdel-Haleem; Yahia, Ibrahim S.; Park, Choonkil 2 2022 On an extension of the operator with Mittag-Leffler kernel. Zbl 1514.34008 Al-Refai, Mohammed; Baleanu, Dumitru 2 2022 Numerical investigation of the nonlinear fractional Ostrovsky equation. Zbl 1504.35388 Wang, Fuzhang; Hou, Enran; Salama, Samir A.; Khater, Mostafa M. A. 2 2022 Investigation to the local fractional Fokas system on Cantor set by a novel technology. Zbl 1507.35332 Wang, Kang-Jia 2 2022 A fractal modification of the Sharma-Tasso-Olver equation and its fractal generalized variational principle. Zbl 1501.35006 Wang, Kang-Jia; Shi, Feng; Liu, Jing-Hua 2 2022 ...and 888 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,271 Authors 50 Chand, Arya Kumar Bedabrata 44 Xi, Lifeng 39 Băleanu, Dumitru I. 38 Navascués, María Antonia 34 Su, Weiyi 32 Viswanathan, Puthan Veedu 31 Abdeljawad, Thabet 27 Wang, Xingyuan 26 Wang, Kang-Jia 25 Chu, Yuming 23 Dai, Meifeng 23 Golmankhaneh, Alireza Khalili 22 Wang, Kangle 21 Rashid, Saima 20 Strichartz, Robert S. 19 Jarad, Fahd 19 Liang, Yongshun 19 Selmi, Bilel 19 Vijender, Nallapu 17 Du, Tingsong 17 Rezapour, Shahram 17 Verma, Saurabh 16 Taqqu, Murad S. 16 Yao, Kui 15 Budak, Hüseyin 15 El-Nabulsi, Rami Ahmad 15 Sabir, Zulqurnain 15 Teplyaev, Alexander 15 Xiao, Boqi 15 Yu, Boming 14 Liu, Fawang 14 Shah, Kamal 14 Wang, Qin 13 Akgül, Ali 13 Drakopoulos, Vasileios 13 Gowrisankar, A. 13 Ma, Chunsheng 13 Ngai, Sze-Man 13 Raja, Muhammad Asif Zahoor 13 Wang, Guodong 13 Yang, Xiao-Jun 12 Etemad, Sina 12 Fraser, Jonathan MacDonald 12 Karaca, Yeliz 12 Ri, Songil 12 Rochon, Dominic 12 Sun, Yu 12 Xue, Yumei 11 Alzabut, Jehad O. 11 Bárány, Balázs 11 Inc, Mustafa 11 Long, Gongbo 11 Ma, Li 11 Veeresha, Pundikala 11 Wu, Min 10 Agarwal, Praveen 10 Deng, Yong 10 Didier, Gustavo 10 Huang, Chengdai 10 Jiang, Kan 10 Jørgensen, Palle E. 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