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 Documents Indexed: 1,260 Publications (since 1993) References Indexed: 984 Publications with 25,570 References. all top 5 Latest Issues 30, No. 2 (2022) 30, No. 1 (2022) 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. 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) 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) 11, No. 1 (2003) 11, Suppl. 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Eugene 8 Khan, Ilyas 8 Navascués, María Antonia 8 Takayasu, Hideki 8 Veneziano, Daniele 7 Ahmad, Hijaz 7 Frame, Michael Lee 7 Li, Wenxia 7 Long, Gongbo 7 Sooppy Nisar, Kottakkaran 7 Strichartz, Robert S. 7 Wang, Kang-Jia 7 Yao, Kui 6 Bory Reyes, Juan 6 Brown, Christopher A. 6 Elías-Zúñiga, Alex 6 Fan, Jiaqi 6 He, Chun-Hui 6 He, Jihuan 6 Jarad, Fahd 6 Jiang, Kan 6 Martínez-Romero, Oscar 6 Olvera Trejo, Daniel 6 Palacios-Pineda, Luis Manuel 6 Xue, Yumei 6 Yang, Xiao-Jun 6 Ye, Qianqian 5 Abdel-Aty, Abdel-Haleem 5 Alrabaiah, Hussam 5 Arfan, Muhammad 5 Boulaaras, Salah Mahmoud 5 Buldyrev, Sergey V. 5 Chen, Hanxin 5 Gu, Jiangwen 5 Huang, Chengdai 5 Khan, Aziz 5 Kim, Jinmyong 5 Lévy Véhel, Jacques 5 Liu, Jiangen 5 Liu, Xiangdong 5 Lu, Jian 5 Luo, Jun 5 Ma, Ying 5 Pietronero, Luciano 5 Rochon, Dominic 5 Roux, Stéphane G. 5 Skordev, Gencho S. 5 Steinhurst, Benjamin 5 Tan, Bo 5 Tian, Li 5 Vrscay, Edward Robert 5 Wang, Xiaoqian 5 Zou, Yuru 4 Atangana, Abdon 4 Baskonus, Haci Mehmet 4 Chen, Chen 4 Demir, Bunyamin 4 Deng, Juan 4 Dewey, T. Gregory 4 Dong, Xinhan 4 Feng, Zhigang 4 Gangal, Anil D. 4 García Guirao, Juan Luis 4 Hammouch, Zakia 4 Herrmann, Hans Jürgen 4 Kapoor, Govind P. 4 Khalid, Aasma 4 Kumam, Poom 4 Li, Yanzhe 4 Li, Yin 4 Liang, Yongshun 4 Liaw, Sy-Sang 4 Liu, Jingcheng 4 Mendivil, Franklin 4 Momani, Shaher M. 4 Peitgen, Heinz-Otto 4 Prasad, Srijanani Anurag 4 Rahman, Matiur 4 Rao, Hui 4 Ri, Songil 4 Saeed, Tareq ...and 2,053 more Authors all top 5 Fields 569 Measure and integration (28-XX) 175 Dynamical systems and ergodic theory (37-XX) 139 Real functions (26-XX) 115 Probability theory and stochastic processes (60-XX) 107 Biology and other natural sciences (92-XX) 103 Ordinary differential equations (34-XX) 100 Numerical analysis (65-XX) 94 Computer science (68-XX) 90 Statistical mechanics, structure of matter (82-XX) 89 Partial differential equations (35-XX) 89 Fluid mechanics (76-XX) 56 Combinatorics (05-XX) 55 Information and communication theory, circuits (94-XX) 46 Statistics (62-XX) 43 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Mechanics of deformable solids (74-XX) 31 Geophysics (86-XX) 28 Number theory (11-XX) 28 Harmonic analysis on Euclidean spaces (42-XX) 26 General and overarching topics; collections (00-XX) 23 Operations research, mathematical programming (90-XX) 21 Classical thermodynamics, heat transfer (80-XX) 21 Systems theory; control (93-XX) 20 Approximations and expansions (41-XX) 15 Optics, electromagnetic theory (78-XX) 14 Difference and functional equations (39-XX) 14 Operator theory (47-XX) 12 Integral equations (45-XX) 11 Functions of a complex variable (30-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Mechanics of particles and systems (70-XX) 9 Convex and discrete geometry (52-XX) 8 General topology (54-XX) 8 Quantum theory (81-XX) 5 Mathematical logic and foundations (03-XX) 5 Integral transforms, operational calculus (44-XX) 5 Astronomy and astrophysics (85-XX) 4 Special functions (33-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Potential theory (31-XX) 3 Functional analysis (46-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 2 Sequences, series, summability (40-XX) 2 Abstract harmonic analysis (43-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 579 Publications have been cited 2,766 times in 1,982 Documents Cited by ▼ Year ▼ Estimators for long-range dependence: An empirical study. Zbl 0864.62061Taqqu, Murad S.; Teverovsky, Vadim; Willinger, Walter 83 1995 The relationship between fractional calculus and fractals. Zbl 0877.28009Tatom, Frank B. 68 1995 Distributed order fractional sub-diffusion. Zbl 1083.60066Naber, Mark 58 2004 Bivariate fractal interpolation functions on grids. Zbl 1088.28502Dalla, Leoni 45 2002 The study of bivariate fractal interpolation functions and creation of fractal interpolated surfaces. Zbl 0908.65005Xie, Heping; Sun, Hongquan 39 1997 Hidden variable bivariate fractal interpolation surfaces. Zbl 1046.28004Chand, A. K. B.; Kapoor, G. P. 37 2003 On the Riemann-Liouville fractional calculus and some recent applications. Zbl 0868.26004Nonnenmacher, Theo F.; Metzler, Ralf 36 1995 Calculus on fractal subsets of real line. I: Formulation. Zbl 1173.28005Parvate, Abhay; Gangal, A. D. 32 2009 A generalized Mandelbrot set for bicomplex numbers. Zbl 0969.37021Rochon, Dominic 32 2000 On Hadamard fractional calculus. Zbl 1371.26009Ma, Li; Li, Changpin 31 2017 Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302Falconer, Kenneth; Miao, Jun 30 2007 Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform. Zbl 1083.65005Stoev, Stilian; Taqqu, Murad S. 30 2004 Cooperative strategies in formation of complex bacterial patterns. Zbl 0869.92002Ben-Jacob, Eshel; Shochet, Ofer; Cohen, Inon; Tenenbaum, Adam; Czirók, Andras; Vicsek, Tamas 29 1995 A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004Barnsley, Michael; Hutchinson, John; Stenflo, Örjan 28 2005 On fractional relaxation. Zbl 1140.82315Hilfer, R. 27 2003 Fractal bases of \(L_p\) spaces. Zbl 1251.28009Navascués, M. A. 27 2012 First-order network coherence and eigentime identity on the weighted Cayley networks. Zbl 1421.05083Dai, Meifeng; Wang, Xiaoqian; Zong, Yue; Zou, Jiahui; Chen, Yufei; Su, Weiyi 27 2017 Multifractal cascade dynamics and turbulent intermittency. Zbl 0927.76044Schertzer, D.; Lovejoy, S.; Schmitt, F.; Chigirinskaya, Y.; Marsan, D. 26 1997 Average geodesic distance of Sierpinski gasket and Sierpinski networks. Zbl 1375.28020Wang, Songjing; Yu, Zhouyu; Xi, Lifeng 26 2017 Topological structure of self-similar sets. Zbl 1075.28005Luo, Jun; Rao, Hui; Tan, Bo 25 2002 Hidden variable vector valued fractal interpolation functions. Zbl 1100.41011Bouboulis, P.; Dalla, L. 24 2005 Analysis of fractional differential equations with multi-orders. Zbl 1176.34008Deng, Weihua; Li, Changpin; Guo, Qian 23 2007 On the dimension of self-similar sets. Zbl 1088.28504Simon, Károly; Solomyak, Boris 21 2002 Modifications at large distances from fractional and fractal arguments. Zbl 1196.28014El-Nabulsi, Rami Ahmad 20 2010 Exact solutions for a class of fractal time random walks. Zbl 0881.60066Hilfer, R. 20 1995 Analysis of \(\mathbb{C}\)-plane fractal images from \(z \leftarrow z^{\alpha} + c\) for \((\alpha < 0)\). Zbl 1211.37059Wang, Xingyuan; Liu, Xiangdong; Zhu, Weiyong; Gu, Shusheng 19 2000 Foundations of fractional dynamics. Zbl 0870.58041Hilfer, R. 18 1995 Certain integral inequalities considering generalized \(m\)-convexity on fractal sets and their applications. Zbl 1434.28018Du, Tingsong; Wang, Hao; Khan, Muhammad Adil; Zhang, Yao 17 2019 Vibration spectra of finitely ramifield, symmetric fractals. Zbl 1160.28302Bajorin, N.; Chen, T.; Dagan, A.; Emmons, C.; Hussein, M.; Khalil, M.; Mody, P.; Steinhurst, B.; Teplyaev, A. 16 2008 Central limit theorem for the log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context. Zbl 1141.62073Moulines, E.; Roueff, F.; Taqqu, Murad S. 16 2007 Fractal image compression. Zbl 0903.68211Fisher, Yuval 16 1994 Nonextensive thermostatics and fractals. Zbl 0870.58098Tsallis, Constantino 16 1995 On a generalized Fatou-Julia theorem in multicomplex spaces. Zbl 1177.30068Garant-Pelletier, V.; Rochon, D. 15 2009 Normal families of bicomplex holomorphic functions. Zbl 1230.30032Charak, K. S.; Rochon, D.; Sharma, N. 15 2009 Box dimensions of {\(\alpha\)}-fractal functions. Zbl 1354.28002Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A. 15 2016 Estimation and simulation of fractal stochastic point processes. Zbl 0881.60044Lowen, Steven B.; Teich, Malvin C. 15 1995 Path properties of the linear multifractional stable motion. Zbl 1304.28010Stoev, Stilian; Taqqu, Murad S. 15 2005 On stability of fractal interpolation. Zbl 0974.28003Feng, Zhigang; Xie, Heping 14 1998 Calculus on fractal curves in \(\mathbb{R}^{n}\). Zbl 1217.28014Parvate, Abhay; Satin, Seema; Gangal, A. D. 14 2011 Calculus on fractal subsets of real line. II: Conjugacy with ordinary calculus. Zbl 1252.28005Parvate, Abhay; Gangal, A. D. 14 2011 Analysis, synthesis, and estimation of fractal-rate stochastic point processes. Zbl 0907.62093Thurner, Stefan; Lowen, Steven B.; Feurstein, Markus C.; Heneghan, Conor; Feichtinger, Hans G.; Teich, Malvin C. 14 1997 A technique in the topology of connected self-similar tiles. Zbl 1304.28009Ngai, Sze-Man; Tang, Tai-Man 14 2004 Dimension analysis of continuous functions with unbounded variation. Zbl 1371.28012Wang, Jun; Yao, Kui 14 2017 Explicit construction of operator scaling Gaussian random fields. Zbl 1233.60027Clausel, M.; Vedel, B. 13 2011 Definition, properties and wavelet analysis of multiscale fractional Brownian motion. Zbl 1142.60329Bardet, Jean-Marc; Bertrand, Pierre 13 2007 On a generalized Fatou-Julia theorem. Zbl 1041.37023Rochon, Dominic 13 2003 Fractal geometry of financial time series. Zbl 0869.62073Evertsz, Carl J. G. 13 1995 Average geodesic distance of Sierpinski carpet. Zbl 1432.28015Zhao, Luming; Wang, Songjing; Xi, Lifeng 13 2017 Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco 12 2003 \(1/f\) noise in a traffic model. Zbl 0906.90072Takayasu, Misako; Takayasu, Hideki 12 1993 Green’s functions on fractals. Zbl 0983.31005Kigami, Jun; Sheldon, Daniel R.; Strichartz, Robert S. 12 2000 Vector random fields with long-range dependence. Zbl 1232.60038Ma, Chunsheng 11 2011 Fractal interpolation functions on post critically finite self-similar sets. Zbl 1196.28019Ruan, Huo-Jun 11 2010 Generalizations of Newton’s method. Zbl 1046.37027Gilbert, William J. 11 2001 Fractal modeling of speech signals. Zbl 1126.94308Lévy Véhel, Jacques; Daoudi, Khalid; Lutton, Evelyne 11 1994 An analysis of U.S. stock price behavior using wavelets. Zbl 0877.90027Ramsey, James B.; Usikov, Daniel; Zaslavsky, George M. 11 1995 On smoothness for a class of fractal interpolation surfaces. Zbl 1302.37020Wang, Hong-Yong 11 2006 Average distance of self-similar fractal trees. Zbl 1432.28007Li, Tingting; Jiang, Kan; Xi, Lifeng 11 2018 Study on the fractal and chaotic features of the Shanghai composite index. Zbl 1250.91084Wen, Fenghua; Li, Zhong; Xie, Chaohua; Shaw, David 11 2012 On the Assouad dimension of graph directed Moran fractals. Zbl 1222.28017Olsen, L. 10 2011 Cantor-type sets in hyperbolic numbers. Zbl 1357.28008Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M. 10 2016 The multifractal dimension functions of homogeneous Moran measure. Zbl 1165.28005Xiao, Jiaqing; Wu, Min 10 2008 Some results of convergence of cubic spline fractal interpolation functions. Zbl 1053.41013Navascués, M. Antonia; Sebastián, M. Victoria 10 2003 Fractal description of anomalous diffusion in dynamical systems. Zbl 0901.58050Klafter, J.; Zumofen, G.; Shlesinger, M. F. 10 1993 The fractal dimension of the Apollonian sphere packing. Zbl 0908.52008Borkovec, M.; de Paris, W.; Peikert, R. 10 1994 Fractal approaches in signal processing. Zbl 0867.94005Lévy-Véhel, Jacques 10 1995 Lipschitz equivalence of McMullen sets. Zbl 1290.28012Li, Boming; Li, Wenxia; Miao, Jun Jie 10 2013 On the automatic selection of the onset of scaling. Zbl 1056.62102Veitch, Darryl; Abry, Patrice; Taqqu, Murad S. 10 2003 The Hosoya index of graphs formed by a fractal graph. Zbl 1434.05039Liu, Jia-bao; Zhao, Jing; Min, Jie; Cao, Jinde 10 2019 Natural cubic spline coalescence hidden variable fractal interpolation surfaces. Zbl 1250.28004Chand, A. K. B. 10 2012 Fractal dimension of certain continuous functions of unbounded variation. Zbl 1371.28005Liang, Y. S.; Su, W. Y. 10 2017 Multifractal cross-correlation analysis based on statistical moments. Zbl 1272.28013Wang, Jing; Shang, Pengjian; Ge, Weijie 9 2012 The connection between the orders of \(p\)-adic calculus and the dimensions of the Weierstrass type function in local fields. Zbl 1136.37321Qiu, Hua; Su, Weiyi 9 2007 A fractal approximation to periodicity. Zbl 1148.28010Navascués, M. A. 9 2006 Beyond classical multifractal analysis using wavelets: uncovering a multiplicative process hidden in the geometrical complexity of diffusion limited aggregates. Zbl 0901.58028Arneodo, A.; Argoul, F.; Muzy, J. F.; Tabard, M.; Bacry, E. 9 1993 Is network traffic self-similar or multifractal? Zbl 0908.60078Taqqu, Murad S.; Teverovsky, Vadim; Willinger, Walter 9 1997 Numerical analysis on the Sierpinski gasket, with applications to Schrödinger equations, wave equation, and Gibbs’ phenomenon. Zbl 1304.28005Coletta, Kevin; Dias, Kealey; Strichartz, Robert S. 9 2004 Rényi function for multifractal random fields. Zbl 1278.28003Leonenko, Nikolai N.; Shieh, Narn-Rueih 9 2013 An user intention mining model based on fractal time series pattern. Zbl 07468599Wu, Shaofei 9 2020 A remark on Wang’s fractal variational principle. Zbl 1434.35267Wang, Kang-Le; He, Chun-Hui 9 2019 K-iterated function system. Zbl 1190.28004Sahu, D. R.; Chakraborty, Anindita; Dubey, R. P. 8 2010 When Thue-Morse meets Koch. Zbl 1110.28007Ma, Jun; Holdener, Judy 8 2005 Lipschitz equivalence of general Sierpinski carpets. Zbl 1159.28004Dai, Meifeng 8 2008 Fractal trees with side branching. Zbl 0907.28005Newman, W. I.; Turcotte, D. L.; Gabrielov, A. M. 8 1997 Convergence of the Weierstrass-Mandelbrot process to fractional Brownian motion. Zbl 0976.60042Pipiras, Vladas; Taqqu, Murad S. 8 2000 Hausdorff measure of Cartesian product of the ternary Cantor set. Zbl 1243.28003Deng, Juan; Rao, Hui; Wen, Zhi-Ying 8 2012 The boundary of the attractor of a recurrent iterated function system. Zbl 1088.28503Dekking, F. M.; van der Wal, P. 8 2002 A new nonlinear fractal interpolation function. Zbl 1432.41001Ri, Songil 8 2017 Horton law in self-similar trees. Zbl 1351.28014Kovchegov, Yevgeniy; Zaliapin, Ilya 8 2016 Fractal trigonometric polynomials for restricted range approximation. Zbl 1351.28009Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K. 8 2016 Construction and analysis of a special one-dimensional continuous function. Zbl 1371.28011Wang, J.; Yao, Kui 8 2017 The quasi-sine Fibonacci hyperbolic dynamic system. Zbl 1192.37066Wang, Xing-Yuan; Ge, Feng-Dan 7 2010 Remarks on dimensions of Cartesian product sets. Zbl 1354.28003Wei, Chun; Wen, Shengyou; Wen, Zhixiong 7 2016 Image compression using affine fractal interpolation on rectangular lattices. Zbl 1158.68051Drakopoulos, V.; Bouboulis, P.; Theodoridis, S. 7 2006 Cubic spline coalescence fractal interpolation through moments. Zbl 1148.28005Chand, A. K. B.; Kapoor, G. P. 7 2007 Composed accelerated escape time algorithm to construct the general Mandelbrot sets. Zbl 1046.37030Liu, Xiangdong; Zhu, Zhiliang; Wang, Guangxing; Zhu, Weiyong 7 2001 On Lévy stable and semistable distributions. Zbl 1045.60010Huillet, Thierry; Porzio, Anna; Alaya, Mohamed Ben 7 2001 Solving the inverse problem for function/image approximation using iterated function systems. II: Algorithm and computations. Zbl 0923.68124Forte, Bruno; Vrscay, Edward R. 7 1994 Multifractal segmentation of images. Zbl 0903.68212Lévy Véhel, Jacques; Mignot, Pascal 7 1994 Mixing in globally chaotic flows: A self-similar process. Zbl 0927.76095Hobbs, D. M.; Alvarez, M. M.; Muzzio, F. J. 7 1997 Some further extensions considering discrete proportional fractional operators. Zbl 07490662Rashid, Saima; Sultana, Sobia; Karaca, Yeliz; Khalid, Aasma; Chu, Yu-Ming 3 2022 Jensen-Mercer inequality and related results in the fractal sense with applications. Zbl 07490644Butt, Saad Ihsan; Yousaf, Saba; Ahmad, Hijaz; Nofal, Taher A. 1 2022 Caputo type fractional operator applied to hepatitis B system. 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Zbl 07465623Yao, Shao-Wen; Ilhan, Esin; Veeresha, P.; Baskonus, Haci Mehmet 1 2021 New computations of Ostrowski-type inequality pertaining to fractal style with applications. Zbl 07465626Al Qurashi, Maysaa; Rashid, Saima; Khalid, Aasma; Karaca, Yeliz; Chu, Yu-Ming 1 2021 Achieving more precise bounds based on double and triple integral as proposed by generalized proportional fractional operators in the Hilfer sense. Zbl 1481.26004Al-Qurashi, Maysaa; Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming 1 2021 Monotonicity and asymptotic properties of solutions for parabolic equations via a given initial value condition on graphs. Zbl 1482.35058Wu, Yiting 1 2021 Study of nonlinear Hirota-Satsuma coupled KdV and coupled mKdV system with time fractional derivative. Zbl 07465629Habib, Siddra; Batool, Amreen; Islam, Asad; Nadeem, Muhammad; Gepreel, Khaled A.; He, Ji-Huan 1 2021 Combined electroosmotic and pressure driven flow in tree-like microchannel network. Zbl 07465631Liu, Fei; Jing, Dalei 1 2021 A fractal model for predicting the effective thermal conductivity of roughened porous media with microscale effect. Zbl 1481.80008Xiao, Boqi; Zhang, Min; Chen, Hanxin; Cao, Jiyin; Long, Gongbo; Zhao, Zheng 1 2021 Low frequency property of a fractal vibration model for a concrete beam. Zbl 1482.74083He, Chun-Hui; Liu, Chao; He, Ji-Huan; Gepreel, Khaled A. 1 2021 A new perspective on the study of the fractal coupled Boussinesq-Burger equation in shallow water. Zbl 07465643Wang, Kang-Jia; Wang, Guo-Dong; Zhu, Hong-Wei 1 2021 The difference between the Hurwitz continued fraction expansions of a complex number and its rational approximations. Zbl 1483.11146He, Yubin; Xiong, Ying 1 2021 Analysis on Weyl-Marchaud fractional derivative for types of fractal interpolation function with fractal dimension. Zbl 07468100Priyanka, T. M. C.; Gowrisankar, A. 1 2021 An investigation on spontaneous imbibition in tree-like branching network with fractal roughened surfaces. Zbl 1482.80005Xiao, Boqi; Liu, Zhenjie; Zhang, Yidan; Liang, Mingchao; Long, Gongbo; Zhao, Zheng 1 2021 Fractal propagation and immunity on network. Zbl 1481.92153Nian, Fuzhong; Yang, Yang; Shi, Yayong 1 2021 A comparative study of semi-analytical methods for solving fractional-order Cauchy reaction-diffusion equation. Zbl 07467680Chu, Yu-Ming; Shah, Nehad Ali; Ahmad, Hijaz; Chung, Jae Dong; Khaled, S. M. 1 2021 A fractal model for effective thermal conductivity of dual-porosity media with randomly distributed tree-like networks. Zbl 1482.80006Zhang, Jun; Wang, Yizhi; Lou, Gang; Kou, Jianlong 1 2021 A novel model for effective thermal conductivity of tree-like branching network with fractal roughened surfaces. Zbl 1482.80003Liu, Yonghui; Li, Zihao; Xiao, Boqi; Chen, Hanxin; Long, Gongbo 1 2021 An user intention mining model based on fractal time series pattern. Zbl 07468599Wu, Shaofei 9 2020 Newton’s-type integral inequalities via local fractional integrals. Zbl 1434.26052Iftikhar, Sabah; Kumam, Poom; Erden, Samet 6 2020 Symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics. Zbl 1434.35278Wang, Gangwei; Liu, Yixing; Wu, Yanbin; Su, Xing 5 2020 The effects of the Riemann-Liouville fractional integral on the box dimension of fractal graphs of Hölder continuous functions. Zbl 1434.26017Wu, Junru 5 2020 Lower Assouad-type dimensions of uniformly perfect sets in doubling metric spaces. Zbl 1434.28014Chen, Haipeng; Wu, Min; Chang, Yuanyang 4 2020 Variational principle for a generalized KdV equation in a fractal space. Zbl 1441.35009Shen, Yue; He, Ji-Huan 4 2020 Fractal networks on Sierpinski-type polygon. Zbl 1445.28019Zeng, Cheng; Xue, Yumei; Zhou, Meng 4 2020 On the weighted fractional operators of a function with respect to another function. Zbl 07468593Jarad, F.; Abdeljawad, T.; Shah, K. 3 2020 New estimates of integral inequalities via generalized proportional fractional integral operator with respect to another function. Zbl 07468609Rashid, Saima; Hammouch, Zakia; Jarad, Fahd; Chu, Yu-Ming 3 2020 Generalized \(h\)-convexity on fractal sets and some generalized Hadamard-type inequalities. Zbl 1434.28036Sun, Wenbing 3 2020 The average weighted path length for a class of hierarchical networks. Zbl 1441.05208Niu, Min; Li, Ruixia 3 2020 A new perspective to study the third-order modified KdV equation on fractal set. Zbl 1445.28012Liu, Jian-Gen; Yang, Xiao-Jun; Feng, Yi-Ying; Cui, Ping 3 2020 A lower bound of topological Hausdorff dimension of fractal squares. Zbl 1445.28021Zhang, Yan-Fang 3 2020 New generalizations in the sense of the weighted non-singular fractional integral operator. Zbl 07468585Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming 2 2020 Mathematical analysis of coupled systems with fractional order boundary conditions. Zbl 07468594Ali, Zeeshan; Shah, Kamal; Zada, Akbar; Kumam, Poom 2 2020 Qualitative study of nonlinear coupled pantograph differential equations of fractional order. Zbl 07468627Ahamad, Israr; Shah, Kamal; Abdeljawad, Thabet; Jarad, Fahd 2 2020 Existence results and stability criteria for ABC-fuzzy-Volterra integro-differential equation. Zbl 1482.45005Khan, Hasib; Gomez-Aguilar, J. F.; Abdeljawad, Thabet; Khan, Aziz 2 2020 Fractal Stokes’ theorem based on integrals on fractal manifolds. Zbl 1434.28009Wu, Junru; Wang, Chengyuan 2 2020 Wada fractal basins of attraction in a zero-stiffness vibration isolation system. Zbl 1434.28044Zhang, Fanhui; Zhang, Yongxiang 2 2020 Construction of fractal surfaces. Zbl 1434.28031Navascués, M. A.; Mohapatra, R. N.; Akhtar, M. N. 2 2020 Average distances of a family of non-p.c.f. self-similar networks. Zbl 1434.05047Zhao, Bing; Gu, Jiangwen; Xi, Lifeng 2 2020 Slow growth rate of the digits in Engel expansions. Zbl 1434.11155Shang, Lei; Wu, Min 2 2020 The scale-free and small-world properties of complex networks on Sierpinski-type hexagon. Zbl 1434.28013Cheng, Kun; Chen, Dirong; Xue, Yumei; Zhang, Qian 2 2020 Multiple exact solutions of the generalized time fractional foam drainage equation. Zbl 1441.34015Shi, Dandan; Zhang, Yufeng; Liu, Wenhao 2 2020 Connectedness of a class of self-affine carpets. Zbl 1441.28009Leung, King Shun; Luo, Jun Jason; Wang, Lian 2 2020 Mean value property of harmonic function on the higher-dimensional Sierpinski gasket. Zbl 1445.28016Wu, Yipeng; Chen, Zhilong; Zhang, Xia; Zhao, Xudong 2 2020 Ahlfors-David regular subsets of fractals. Zbl 1445.28013Pan, Yue; Xiong, Ying 2 2020 Box dimensions of the Riemann-Liouville fractional integral of Hölder continuous multivariate functions. Zbl 1445.26005Lei, Jing; Liu, Kangjie; Dai, Yingzi 2 2020 Using a prior estimate method to investigate sequential hybrid fractional differential equations. Zbl 07468586Nazir, Ghazala; Shah, Kamal; Abdeljawad, Thabet; Khalil, Hammad; Khan, Rahmat Ali 1 2020 Existence and stability analysis of solutions for fractional Langevin equation with nonlocal integral and anti-periodic-type boundary conditions. Zbl 07468588Devi, Amita; Kumar, Anoop; Abdeljawad, Thabet; Khan, Aziz 1 2020 Piecewise optimal fractional reproducing kernel solution and convergence analysis for the Atangana-Baleanu-Caputo model of the Lienard’s equation. Zbl 07468589Momani, Shaher; Arqub, Omar Abu; Maayah, Banan 1 2020 Digital imaging based on fractal theory and its spatial dimensionality. Zbl 07468596Tian, Yuan; Cui, Gaoyuan; Morris, Harry 1 2020 Applicability of topological degree theory to evolution equation with proportional delay. Zbl 07468610Sher, Muhammad; Shah, Kamal; Chu, Yu-Ming; Khan, Rahmat Ali 1 2020 Mathematical and statistical analysis of RL and RC fractional-order circuits. Zbl 07468612Sheikh, Nadeem Ahmad; Ching, Dennis Ling Chuan; Ullah, Sami; Khan, Ilyas 1 2020 A novel \(R/S\) fractal analysis and wavelet entropy characterization approach for robust forecasting based on self-similar time series modeling. Zbl 1482.91200Karaca, Yeliz; Baleanu, Dumitru 1 2020 On explicit wave solutions of the fractional nonlinear DSW system via the modified Khater method. Zbl 1482.76026Yue, Chen; Lu, Dianchen; Khater, Mostafa M. A.; Abdel-Aty, Abdel-Haleem; Alharbi, W.; Attia, Raghda A. M. 1 2020 Existence of 3-weak solutions for a new class of an overdetermined system of fractional partial integro-differential equations. Zbl 1483.35312Boulaaras, Salah; Guefaifia, Rafik; Alharbi, Asma; Cherif, Bahri 1 2020 Analysis of dengue fever outbreak by generalized fractional derivative. Zbl 07468620Bosch, Paul; Gómez-Aguilar, J. F.; Rodríguez, José M.; Sigarreta, José M. 1 2020 The numerical treatment of nonlinear fractal-fractional 2D Emden-Fowler equation utilizing 2D Chelyshkov polynomials. Zbl 07468624Hosseininia, M.; Heydari, M. H.; Avazzadeh, Z. 1 2020 Cauchy problems with fractal-fractional operators and applications to groundwater dynamics. Zbl 1483.35315Atangana, Abdon; Doungmo Goufo, Emile Franc 1 2020 Atangana-Seda numerical scheme for labyrinth attractor with new differential and integral operators. Zbl 07468626Atangana, Abdon; İğret Araz, Seda 1 2020 Applications of bi-framelet systems for solving fractional order differential equations. Zbl 1482.65107Mohammad, Mutaz; Cattani, Carlo 1 2020 Small-world and scale-free properties of the \(n\)-dimensional Sierpinski cube networks. Zbl 1434.28043Zeng, Cheng; Zhou, Meng; Xue, Yumei 1 2020 Some remarks on fractional integral of one-dimensional continuous functions. Zbl 1434.26018Yao, Jia; Chen, Ying; Li, Junqiao; Wang, Bin 1 2020 A class of spectral Moran measures on \(\mathbb{R} \). Zbl 1434.28002Liu, Zong-Sheng; Dong, Xin-Han; Zhang, Peng-Fei 1 2020 Hausdorff dimensions of some exceptional sets in the first Ostrogradsky series. Zbl 1434.28020Feng, Yan; Tan, Bo 1 2020 Hölder continuity and box dimension for the Weyl fractional integral. Zbl 1434.26016Tian, Long 1 2020 The growth rate of the digits in the Lüroth expansions. Zbl 1441.11188Lü, Meiying 1 2020 A general comparison principle for Caputo fractional-order ordinary differential equations. Zbl 1441.34018Wu, Cong 1 2020 Dirichlet problem of Poisson equations and variational principle on a type of fractal sets. Zbl 1445.28017Wu, Yipeng; Yao, Kui; Mu, Lei; Chen, Zhilong 1 2020 Family of shape preserving fractal-like Bézier curves. Zbl 1445.28014Reddy, K. M.; Saravana Kumar, G.; Chand, A. K. B. 1 2020 ...and 479 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,068 Authors 41 Chand, Arya Kumar Bedabrata 32 Navascués, María Antonia 26 Viswanathan, Puthan Veedu 26 Xi, Lifeng 24 Su, Weiyi 23 Wang, Xingyuan 17 Băleanu, Dumitru I. 17 Strichartz, Robert S. 16 Taqqu, Murad S. 16 Vijender, Nallapu 13 Yao, Kui 12 Dai, Meifeng 12 El-Nabulsi, Rami Ahmad 12 Golmankhaneh, Alireza Khalili 11 Liu, Fawang 11 Rochon, Dominic 10 Bárány, Balázs 10 Fraser, Jonathan MacDonald 10 Loridant, Benoit 10 Ma, Chunsheng 10 Teplyaev, Alexander 10 Wang, Qin 10 Yu, Boming 9 Didier, Gustavo 9 Drakopoulos, Vasileios 9 Leonenko, Nikolai N. 9 Liang, Yongshun 9 Ngai, Sze-Man 9 Selmi, Bilel 9 Thuswaldner, Jörg Maximilian 9 Yang, Xiao-Jun 8 Anh, Vo V. 8 Bardet, Jean-Marc 8 Bouboulis, Pantelis 8 Dalla, Leoni 8 Fan, Jiaqi 8 Gorenflo, Rudolf 8 Jørgensen, Palle E. T. 8 Lévy Véhel, Jacques 8 Machado, José António Tenreiro 8 Mainardi, Francesco 8 Meerschaert, Mark Marvin 8 Stanley, H. Eugene 8 Telesca, Luciano 8 Xiao, Boqi 8 Xue, Yumei 7 Arneodo, Alain 7 Chu, Yuming 7 Falconer, Kenneth J. 7 Hilfer, Rudolf 7 Jiang, Kan 7 Katiyar, Saurabh Kumar 7 Kovchegov, Yevgeniy V. 7 Luo, Jun 7 Montoya, Fausto 7 Pastor, Gerardo 7 Prasad, M. Guru Prem 7 Ri, Songil 7 Romera, Miguel 7 Ruan, Huo-Jun 7 Sandev, Trifce 7 Stenflo, Orjan 7 Turner, Ian William 7 Wu, Bo 7 Yun, Cholhui 6 Balankin, Alexander S. 6 Bory Reyes, Juan 6 Gu, Jiangwen 6 Ju, Tingting 6 Käenmäki, Antti 6 Li, Changpin 6 Li, Wenxia 6 Li, Yin 6 Long, Gongbo 6 Miculescu, Radu 6 Morris, Ian D. 6 Qiu, Hua 6 Rams, Michał 6 Saxena, Ram Kishore 6 Sebastián, María Victoria 6 Shahverdian, Ashot Yu. 6 Simon, Károly 6 Sun, Yu 6 Vâjiac, Adrian I. 6 Ye, Qianqian 6 Zaliapin, Ilya 6 Zhou, Songping 5 Abdo, Mohammed Salem 5 Agarwal, Ravi P. 5 Akhtar, Md. Nasim 5 Akiyama, Shigeki 5 Ben Slimane, Mourad 5 Berg, Kimmo 5 Boulaaras, Salah Mahmoud 5 Chen, Yangquan 5 Gangal, Anil D. 5 Gdawiec, Krzysztof 5 Gowrisankar, A. 5 Haq, Sirajul 5 Hussain, Manzoor ...and 2,968 more Authors all top 5 Cited in 406 Journals 358 Fractals 109 Chaos, Solitons and Fractals 52 Physica A 50 Journal of Mathematical Analysis and Applications 42 Applied Mathematics and Computation 35 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 30 Journal of Statistical Physics 29 Chaos 28 Nonlinear Dynamics 25 Fractional Calculus & Applied Analysis 25 Communications in Nonlinear Science and Numerical Simulation 24 Computers & Mathematics with Applications 19 Journal of Mathematical Physics 19 Physica D 18 Mathematical Problems in Engineering 18 Journal of Statistical Mechanics: Theory and Experiment 16 Abstract and Applied Analysis 16 Advances in Difference Equations 15 Physics Letters. 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New Series 5 Experimental Mathematics 5 Journal of Inequalities and Applications 5 International Journal of Theoretical and Applied Finance 5 Advances in Mathematical Physics 5 Statistics and Computing 5 Mathematics 5 Journal of Function Spaces 4 Advances in Applied Probability 4 Applicable Analysis 4 Computer Methods in Applied Mechanics and Engineering 4 Mathematics of Computation 4 The Annals of Statistics 4 Journal of Econometrics 4 Journal of Functional Analysis 4 Topology and its Applications 4 Journal of Scientific Computing 4 Forum Mathematicum 4 The Journal of Geometric Analysis 4 Applied and Computational Harmonic Analysis 4 Discrete and Continuous Dynamical Systems 4 Journal of Applied Statistics 4 Statistical Inference for Stochastic Processes ...and 306 more Journals all top 5 Cited in 61 Fields 707 Measure and integration (28-XX) 280 Dynamical systems and ergodic theory (37-XX) 277 Probability theory and stochastic processes (60-XX) 272 Real functions (26-XX) 232 Partial differential equations (35-XX) 217 Numerical analysis (65-XX) 187 Statistics (62-XX) 167 Ordinary differential equations (34-XX) 132 Statistical mechanics, structure of matter (82-XX) 105 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 102 Biology and other natural sciences (92-XX) 93 Approximations and expansions (41-XX) 86 Fluid mechanics (76-XX) 85 Computer science (68-XX) 82 Combinatorics (05-XX) 76 Information and communication theory, circuits (94-XX) 75 Harmonic analysis on Euclidean spaces (42-XX) 55 Number theory (11-XX) 54 Operator theory (47-XX) 42 Special functions (33-XX) 42 Mechanics of deformable solids (74-XX) 41 Functions of a complex variable (30-XX) 38 Geophysics (86-XX) 37 General topology (54-XX) 36 Operations research, mathematical programming (90-XX) 34 Quantum theory (81-XX) 32 Convex and discrete geometry (52-XX) 31 Functional analysis (46-XX) 31 Systems theory; control (93-XX) 28 Potential theory (31-XX) 23 Calculus of variations and optimal control; optimization (49-XX) 23 Classical thermodynamics, heat transfer (80-XX) 19 Integral equations (45-XX) 18 Integral transforms, operational calculus (44-XX) 18 Global analysis, analysis on manifolds (58-XX) 18 Mechanics of particles and systems (70-XX) 15 Difference and functional equations (39-XX) 15 Relativity and gravitational theory (83-XX) 12 Differential geometry (53-XX) 11 Optics, electromagnetic theory (78-XX) 10 General and overarching topics; collections (00-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 8 Several complex variables and analytic spaces (32-XX) 7 Mathematical logic and foundations (03-XX) 7 Group theory and generalizations (20-XX) 7 Topological groups, Lie groups (22-XX) 7 Abstract harmonic analysis (43-XX) 7 Geometry (51-XX) 6 Astronomy and astrophysics (85-XX) 5 Mathematics education (97-XX) 4 History and biography (01-XX) 4 Algebraic geometry (14-XX) 3 Algebraic topology (55-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Sequences, series, summability (40-XX) 2 Manifolds and cell complexes (57-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) Citations by Year