# zbMATH — the first resource for mathematics

## 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: 883 Publications (since 1993) References Indexed: 611 Publications with 11,979 References.
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#### Authors

 19 Xi, Lifeng 11 Dai, Meifeng 11 Su, Weiyi 10 Chand, Arya Kumar Bedabrata 10 Havlin, Shlomo 10 Taqqu, Murad S. 10 Wang, Xingyuan 9 Giona, Massimiliano 8 Navascués, María Antonia 8 Stanley, H. Eugene 8 Takayasu, Hideki 8 Veneziano, Daniele 8 Wang, Qin 8 Yu, Boming 7 Frame, Michael L. 7 Li, Wenxia 6 Brown, Christopher A. 6 Strichartz, Robert S. 6 Yao, Kui 6 Ye, Qianqian 5 Bory Reyes, Juan 5 Buldyrev, Sergey V. 5 Gu, Jiangwen 5 Jiang, Kan 5 Lévy Véhel, Jacques 5 Liu, Xiangdong 5 Pietronero, Luciano 5 Rochon, Dominic 5 Roux, Stéphane G. 5 Skordev, Gencho S. 5 Steinhurst, Benjamin 5 Vrscay, Edward Robert 5 Wang, Xiaoqian 5 Xue, Yumei 4 Demir, Bunyamin 4 Deng, Juan 4 Dewey, T. Gregory 4 Feng, Zhigang 4 Gangal, Anil D. 4 Herrmann, Hans Jürgen 4 Kapoor, Govind P. 4 Li, Yin 4 Liaw, Sy-Sang 4 Liu, Jingcheng 4 Lu, Jian 4 Luo, Jun 4 Mendivil, Franklin 4 Peitgen, Heinz-Otto 4 Rao, Hui 4 Shlesinger, Michael F. 4 Sun, Yu 4 Tan, Bo 4 Tian, Li 4 Tosan, Eric 4 Uthayakumar, Ramasamy 4 Xie, Heping 4 Zhu, Jiali 4 Zhu, Weiyong 4 Zou, Yuru 3 Barbé, André M. 3 Ben Slimane, Mourad 3 Bunde, Armin 3 Cai, Jianchao 3 Chen, Jin 3 Chen, Yufei 3 Coniglio, Antonio 3 Datta, Dhurjati Prasad 3 Dekking, Frederik Michel 3 Ding, Jiu 3 Dong, Xinhan 3 Evertsz, Carl J. G. 3 Family, Fereydoon 3 Frankel, Norman E. 3 Furcolo, Pierluigi 3 Ghosh, Dipak 3 Hansen, Alex 3 Hilfer, Rudolf 3 Huillet, Thierry E. 3 Jestczemski, F. 3 Jøssang, Torstein 3 Ju, Tingting 3 Kim, Jinmyong 3 Kim, Kyungsik 3 La Torre, Davide 3 Lanski, Jennifer 3 Li, Changpin 3 Li, Yanzhe 3 Liang, Yongshun 3 Meakin, Paul 3 Miyazima, Sasuke 3 Monro, Donald M. 3 Mun, Hakmyong 3 Palagallo, Judith A. 3 Pan, Xuezai 3 Parvate, Abhay 3 Prasad, Srijanani Anurag 3 Puente, Carlos E. 3 Ren, Xiaomin 3 Ri, Songil 3 Roman, H. Eduardo ...and 1,306 more Authors
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#### Fields

 472 Measure and integration (28-XX) 149 Dynamical systems and ergodic theory (37-XX) 97 Probability theory and stochastic processes (60-XX) 83 Statistical mechanics, structure of matter (82-XX) 71 Biology and other natural sciences (92-XX) 62 Computer science (68-XX) 53 Real functions (26-XX) 46 Fluid mechanics (76-XX) 39 Numerical analysis (65-XX) 39 Information and communication theory, circuits (94-XX) 38 Combinatorics (05-XX) 32 Statistics (62-XX) 30 Partial differential equations (35-XX) 25 Geophysics (86-XX) 24 Harmonic analysis on Euclidean spaces (42-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 20 Number theory (11-XX) 20 Mechanics of deformable solids (74-XX) 19 General and overarching topics; collections (00-XX) 18 Ordinary differential equations (34-XX) 14 Approximations and expansions (41-XX) 11 Operations research, mathematical programming (90-XX) 10 Global analysis, analysis on manifolds (58-XX) 8 Functions of a complex variable (30-XX) 7 Convex and discrete geometry (52-XX) 7 General topology (54-XX) 7 Optics, electromagnetic theory (78-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Difference and functional equations (39-XX) 5 Quantum theory (81-XX) 5 Astronomy and astrophysics (85-XX) 4 Mechanics of particles and systems (70-XX) 3 Functional analysis (46-XX) 3 Differential geometry (53-XX) 3 Relativity and gravitational theory (83-XX) 2 Mathematical logic and foundations (03-XX) 2 Potential theory (31-XX) 2 Special functions (33-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Operator theory (47-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 History and biography (01-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX)

#### Citations contained in zbMATH Open

446 Publications have been cited 2,276 times in 1,703 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
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
A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004
Barnsley, Michael; Hutchinson, John; Stenflo, Örjan
2005
Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302
Falconer, Kenneth; Miao, Jun
2007
Calculus on fractal subsets of real line. I: Formulation. Zbl 1173.28005
Parvate, Abhay; Gangal, A. D.
2009
Topological structure of self-similar sets. Zbl 1075.28005
Luo, Jun; Rao, Hui; Tan, Bo
2002
Multifractal cascade dynamics and turbulent intermittency. Zbl 0927.76044
Schertzer, D.; Lovejoy, S.; Schmitt, F.; Chigirinskaya, Y.; Marsan, D.
1997
On Hadamard fractional calculus. Zbl 1371.26009
Ma, Li; Li, Changpin
2017
On fractional relaxation. Zbl 1140.82315
Hilfer, R.
2003
Fractal bases of $$L_p$$ spaces. Zbl 1251.28009
Navascués, M. A.
2012
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
Hidden variable vector valued fractal interpolation functions. Zbl 1100.41011
Bouboulis, P.; Dalla, L.
2005
On the dimension of self-similar sets. Zbl 1088.28504
Simon, Károly; Solomyak, Boris
2002
Analysis of fractional differential equations with multi-orders. Zbl 1176.34008
Deng, Weihua; Li, Changpin; Guo, Qian
2007
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
Exact solutions for a class of fractal time random walks. Zbl 0881.60066
Hilfer, R.
1995
Foundations of fractional dynamics. Zbl 0870.58041
Hilfer, R.
1995
Modifications at large distances from fractional and fractal arguments. Zbl 1196.28014
2010
Nonextensive thermostatics and fractals. Zbl 0870.58098
Tsallis, Constantino
1995
Average geodesic distance of Sierpinski gasket and Sierpinski networks. Zbl 1375.28020
Wang, Songjing; Yu, Zhouyu; Xi, Lifeng
2017
Estimation and simulation of fractal stochastic point processes. Zbl 0881.60044
Lowen, Steven B.; Teich, Malvin C.
1995
Fractal image compression. Zbl 0903.68211
Fisher, Yuval
1994
On a generalized Fatou-Julia theorem in multicomplex spaces. Zbl 1177.30068
Garant-Pelletier, V.; Rochon, D.
2009
Normal families of bicomplex holomorphic functions. Zbl 1230.30032
Charak, K. S.; Rochon, D.; Sharma, N.
2009
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
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
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
Explicit construction of operator scaling Gaussian random fields. Zbl 1233.60027
Clausel, M.; Vedel, B.
2011
Definition, properties and wavelet analysis of multiscale fractional Brownian motion. Zbl 1142.60329
Bardet, Jean-Marc; Bertrand, Pierre
2007
Box dimensions of {$$\alpha$$}-fractal functions. Zbl 1354.28002
Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A.
2016
$$1/f$$ noise in a traffic model. Zbl 0906.90072
Takayasu, Misako; Takayasu, Hideki
1993
Green’s functions on fractals. Zbl 0983.31005
Kigami, Jun; Sheldon, Daniel R.; Strichartz, Robert S.
2000
On stability of fractal interpolation. Zbl 0974.28003
Feng, Zhigang; Xie, Heping
1998
Calculus on fractal subsets of real line. II: Conjugacy with ordinary calculus. Zbl 1252.28005
Parvate, Abhay; Gangal, A. D.
2011
Generalizations of Newton’s method. Zbl 1046.37027
Gilbert, William J.
2001
Calculus on fractal curves in $$\mathbb{R}^{n}$$. Zbl 1217.28014
Parvate, Abhay; Satin, Seema; Gangal, A. D.
2011
Vector random fields with long-range dependence. Zbl 1232.60038
Ma, Chunsheng
2011
Fractal geometry of financial time series. Zbl 0869.62073
Evertsz, Carl J. G.
1995
An analysis of U.S. stock price behavior using wavelets. Zbl 0877.90027
Ramsey, James B.; Usikov, Daniel; Zaslavsky, George M.
1995
Some results of convergence of cubic spline fractal interpolation functions. Zbl 1053.41013
Navascués, M. Antonia; Sebastián, M. Victoria
2003
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
2003
On the automatic selection of the onset of scaling. Zbl 1056.62102
Veitch, Darryl; Abry, Patrice; Taqqu, Murad S.
2003
Natural cubic spline coalescence hidden variable fractal interpolation surfaces. Zbl 1250.28004
Chand, A. K. B.
2012
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 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
Dimension analysis of continuous functions with unbounded variation. Zbl 1371.28012
Wang, Jun; Yao, Kui
2017
Lipschitz equivalence of McMullen sets. Zbl 1290.28012
Li, Boming; Li, Wenxia; Miao, Jun Jie
2013
On the Assouad dimension of graph directed Moran fractals. Zbl 1222.28017
Olsen, L.
2011
Fractal approaches in signal processing. Zbl 0867.94005
Lévy-Véhel, Jacques
1995
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
Is network traffic self-similar or multifractal? Zbl 0908.60078
1997
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
A fractal approximation to periodicity. Zbl 1148.28010
Navascués, M. A.
2006
Fractal dimension of certain continuous functions of unbounded variation. Zbl 1371.28005
Liang, Y. S.; Su, W. Y.
2017
On smoothness for a class of fractal interpolation surfaces. Zbl 1302.37020
Wang, Hong-Yong
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
Average geodesic distance of Sierpinski carpet. Zbl 1432.28015
Zhao, Luming; Wang, Songjing; Xi, Lifeng
2017
The Hosoya index of graphs formed by a fractal graph. Zbl 1434.05039
Liu, Jia-bao; Zhao, Jing; Min, Jie; Cao, Jinde
2019
The boundary of the attractor of a recurrent iterated function system. Zbl 1088.28503
Dekking, F. M.; van der Wal, P.
2002
Fractal modeling of speech signals. Zbl 1126.94308
Lévy Véhel, Jacques; Daoudi, Khalid; Lutton, Evelyne
1994
Fractal trees with side branching. Zbl 0907.28005
Newman, W. I.; Turcotte, D. L.; Gabrielov, A. M.
1997
Convergence of the Weierstrass-Mandelbrot process to fractional Brownian motion. Zbl 0976.60042
2000
Fractal interpolation functions on post critically finite self-similar sets. Zbl 1196.28019
Ruan, Huo-Jun
2010
K-iterated function system. Zbl 1190.28004
Sahu, D. R.; Chakraborty, Anindita; Dubey, R. P.
2010
Horton law in self-similar trees. Zbl 1351.28014
Kovchegov, Yevgeniy; Zaliapin, Ilya
2016
Lipschitz equivalence of general Sierpinski carpets. Zbl 1159.28004
Dai, Meifeng
2008
Rényi function for multifractal random fields. Zbl 1278.28003
Leonenko, Nikolai N.; Shieh, Narn-Rueih
2013
Average distance of self-similar fractal trees. Zbl 1432.28007
Li, Tingting; Jiang, Kan; Xi, Lifeng
2018
On Lévy stable and semistable distributions. Zbl 1045.60010
Huillet, Thierry; Porzio, Anna; Alaya, Mohamed Ben
2001
When Thue-Morse meets Koch. Zbl 1110.28007
Ma, Jun; Holdener, Judy
2005
The fractal geometry of the Mandelbrot set. II: How to count and how to add. Zbl 0929.37016
Devaney, Robert L.
1995
Statistical and linguistic features of DNA sequences. Zbl 0878.92007
Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Peng, C.-K.; Simons, M.; Stanley, H. E.
1995
Long range correlation in human writings. Zbl 0876.00022
Schenkel, Alain; Zhang, Jun; Zhang, Yi-Cheng
1993
Solving the inverse problem for function/image approximation using iterated function systems. II: Algorithm and computations. Zbl 0923.68124
Forte, Bruno; Vrscay, Edward R.
1994
Multifractal segmentation of images. Zbl 0903.68212
Lévy Véhel, Jacques; Mignot, Pascal
1994
Mixing in globally chaotic flows: A self-similar process. Zbl 0927.76095
Hobbs, D. M.; Alvarez, M. M.; Muzzio, F. J.
1997
Image compression using affine fractal interpolation on rectangular lattices. Zbl 1158.68051
Drakopoulos, V.; Bouboulis, P.; Theodoridis, S.
2006
Cubic spline coalescence fractal interpolation through moments. Zbl 1148.28005
Chand, A. K. B.; Kapoor, G. P.
2007
The quasi-sine Fibonacci hyperbolic dynamic system. Zbl 1192.37066
Wang, Xing-Yuan; Ge, Feng-Dan
2010
Fractal trigonometric polynomials for restricted range approximation. Zbl 1351.28009
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016
Remarks on dimensions of Cartesian product sets. Zbl 1354.28003
Wei, Chun; Wen, Shengyou; Wen, Zhixiong
2016
Cantor-type sets in hyperbolic numbers. Zbl 1357.28008
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016
Hausdorff measure of Cartesian product of the ternary Cantor set. Zbl 1243.28003
Deng, Juan; Rao, Hui; Wen, Zhi-Ying
2012
Spectral analysis for weighted iterated triangulations of graphs. Zbl 1432.35058
Chen, Yufei; Dai, Meifeng; Wang, Xiaoqian; Sun, Yu; Su, Weiyi
2018
CAPM, risk and portfolio selection in “$$\alpha$$-stable markets”. Zbl 1047.91531
Belkacem, Lotfi; Lévy-Véhel, Jacques; Walter, Christian
2000
Composed accelerated escape time algorithm to construct the general Mandelbrot sets. Zbl 1046.37030
Liu, Xiangdong; Zhu, Zhiliang; Wang, Guangxing; Zhu, Weiyong
2001
The Newton-Raphson method and adaptive ODE solvers. Zbl 1219.65049
Schneebeli, Hans Rudolf; Wihler, Thomas P.
2011
Multifractal cross-correlation analysis based on statistical moments. Zbl 1272.28013
Wang, Jing; Shang, Pengjian; Ge, Weijie
2012
Symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics. Zbl 1434.35278
Wang, Gangwei; Liu, Yixing; Wu, Yanbin; Su, Xing
2020
Lower Assouad-type dimensions of uniformly perfect sets in doubling metric spaces. Zbl 1434.28014
Chen, Haipeng; Wu, Min; Chang, Yuanyang
2020
Fractal Stokes’ theorem based on integrals on fractal manifolds. Zbl 1434.28009
Wu, Junru; Wang, Chengyuan
2020
Slow growth rate of the digits in Engel expansions. Zbl 1434.11155
Shang, Lei; Wu, Min
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
Connectedness of a class of self-affine carpets. Zbl 1441.28009
Leung, King Shun; Luo, Jun Jason; Wang, Lian
2020
A class of spectral Moran measures on $$\mathbb{R}$$. Zbl 1434.28002
Liu, Zong-Sheng; Dong, Xin-Han; Zhang, Peng-Fei
2020
Construction of fractal surfaces. Zbl 1434.28031
Navascués, M. A.; Mohapatra, R. N.; Akhtar, M. N.
2020
Ahlfors-David regular subsets of fractals. Zbl 1445.28013
Pan, Yue; Xiong, Ying
2020
A lower bound of topological Hausdorff dimension of fractal squares. Zbl 1445.28021
Zhang, Yan-Fang
2020
The Hosoya index of graphs formed by a fractal graph. Zbl 1434.05039
Liu, Jia-bao; Zhao, Jing; Min, Jie; Cao, Jinde
2019
Certain integral inequalities considering generalized $$m$$-convexity on fractal sets and their applications. Zbl 1434.28018
2019
Blow-up phenomena profile for Hadamard fractional differential systems in finite time. Zbl 1435.34015
Ma, Li
2019
Comparison theorems for Caputo-Hadamard fractional differential equations. Zbl 1433.34012
Ma, Li
2019
A remark on Wang’s fractal variational principle. Zbl 1434.35267
Wang, Kang-Le; He, Chun-Hui
2019
Eccentric distance sum of Sierpiński gasket and Sierpiński network. Zbl 1433.28009
Chen, Jin; He, Long; Wang, Qin
2019
Geodesics of higher-dimensional Sierpinski gasket. Zbl 1433.28015
Gu, Jiangwen; Ye, Qianqian; Xi, Lifeng
2019
He-Elzaki method for spatial diffusion of biological population. Zbl 1434.35277
2019
Average geodesic distance on Sierpinski hexagon and Sierpinski hexagon networks. Zbl 1434.28046
Zhu, Jiali; Tian, Li; Wang, Qin
2019
Trapping problem of the weighted scale-free triangulation networks for biased walks. Zbl 1433.05286
Dai, Meifeng; Ju, Tingting; Zong, Yue; He, Jiaojiao; Shen, Chunyu; Su, Weiyi
2019
Divisible sandpile on Sierpinski gasket graphs. Zbl 1433.28016
Huss, Wilfried; Sava-huss, Ecaterina
2019
Average geodesic distance of node-weighted Sierpinski networks. Zbl 1434.28039
Xi, Lifeng; Ye, Qianqian; Gu, Jiangwen
2019
The trapping problem of weighted $$(2, 2)$$-flower networks with the same weight sequence. Zbl 1434.05141
Xing, Changming
2019
Non-spectrality of the planar self-affine measures with four-element digit sets. Zbl 1434.28034
Su, Juan; Liu, Yao; Liu, Jing-Cheng
2019
Asymptotic formula of average distances on fractal networks modeled by Sierpinski tetrahedron. Zbl 1434.28017
Deng, Juan; Wang, Qin
2019
Geodesic distance on Lalley-Gatzouras carpets. Zbl 1434.28038
Wang, Qin; Zhu, Yizhe; Pei, Qiyang; Xi, Lifeng
2019
Parametric iterative function system for the continuum growth: Cantor set case. Zbl 1434.28022
Gutiérrez-Hernández, Sebastián; Bory-Reyes, Juan
2019
A revisit to $$\alpha$$-fractal function and box dimension of its graph. Zbl 1434.28037
Verma, S.; Viswanathan, P.
2019
Average distance of substitution networks. Zbl 1434.05045
Ye, Qianqian; Xi, Lifeng
2019
Conjectures about simple dynamics for some real Newton maps on $$\mathbb{R}^2$$. Zbl 1434.34051
De Leo, Roberto
2019
Construction of nonlinear hidden variable fractal interpolation functions and their stability. Zbl 1435.28012
Kim, Jinmyong; Kim, Hyonjin; Mun, Hakmyong
2019
Eigentime identities of fractal flower networks. Zbl 1433.05290
Ye, Qianqian; Gu, Jiangwen; Xi, Lifeng
2019
Scale-free and small-world properties of a special hierarchical network. Zbl 1433.05294
Wang, Daohua; Xue, Yumei; Zhang, Qian; Niu, Min
2019
Box dimension of a nonlinear fractal interpolation curve. Zbl 1433.28027
Ri, Song-Il
2019
Fractal sets in the field of $$p$$-adic analogue of the complex numbers. Zbl 1433.28019
Li, Yin; Qiu, Hua
2019
The cardinality of orthogonal exponential functions on the spatial Sierpinski gasket. Zbl 1433.28038
Zheng, Jia; Liu, Jing-Cheng; Chen, Ming-Liang
2019
Box dimension of Weyl-Marchaud fractional derivative of linear fractal interpolation functions. Zbl 1433.28025
Peng, Wen Liang; Yao, Kui; Zhang, Xia; Yao, Jia
2019
Spectral property of certain Moran measures with three-element digit sets. Zbl 1433.26005
Fu, Xiu-Qun; Dong, Xin-Han; Liu, Zong-Sheng; Wang, Zhi-Yong
2019
Arithmetic on Moran sets. Zbl 1434.26071
Ren, Xiaomin; Tian, Li; Zhu, Jiali; Jiang, Kan
2019
Shape preserving rational quartic fractal functions. Zbl 1434.28024
Katiyar, S. K.; Chand, A. K. B.
2019
Average distance of self-similar fractal trees. Zbl 1432.28007
Li, Tingting; Jiang, Kan; Xi, Lifeng
2018
Spectral analysis for weighted iterated triangulations of graphs. Zbl 1432.35058
Chen, Yufei; Dai, Meifeng; Wang, Xiaoqian; Sun, Yu; Su, Weiyi
2018
Scaling properties of first return time on weighted transfractals $$(1, 3)$$-flowers. Zbl 1433.26006
Dai, Meifeng; Chi, Huijia; Wu, Xianbin; Zong, Yue; Feng, Wenjing; Su, Weiyi
2018
A construction of the scrambled set with full Hausdorff dimension for beta-transformations. Zbl 1432.28008
Liu, Wei-Bin; Huang, Cheng; Li, Mei-Hua; Wang, Shuailing
2018
Boundary value problem involving the $$p$$-Laplacian on the Sierpiński gasket. Zbl 1432.28010
2018
Cutting self-similar space-filling sphere packings. Zbl 1432.05027
Stäger, D. V.; Herrmann, H. J.
2018
Geodesics of the Sierpinski gasket. Zbl 1433.28028
Saltan, Mustafa; Özdemir, Yunus; Demir, Bünyamin
2018
The Hadamard fractional calculus of a fractal function. Zbl 1433.26009
Wu, Yipeng; Yao, Kui; Zhang, Xia
2018
Bernstein fractal rational approximants with no condition on scaling vectors. Zbl 1433.28031
Vijender, N.
2018
On the exact convex hull of IFS fractals. Zbl 1432.28012
Vass, József
2018
Basic topological structure of fast basins. Zbl 1432.37054
Barnsley, Michael F.; Leśniak, Krzysztof; Rypka, Miroslav
2018
Multifractal analysis of the Birkhoff sums of Saint-Petersburg potential. Zbl 1433.37024
Kim, Dong Han; Liao, Lingmin; Rams, Michał; Wang, Bao-wei
2018
Asymptotic formula of eccentric distance sum for Vicsek network. Zbl 1433.28036
Ye, Qianqian; He, Long; Wang, Qin; Xi, Lifeng
2018
Multifractal analysis of one-dimensional biased walks. Zbl 1433.60021
Chen, Yufei; Dai, Meifeng; Wang, Xiaoqian; Sun, Yu; Su, Weiyi
2018
Intersections of translation of a class of Sierpinski carpets. Zbl 1433.28020
Lu, Jian; Tan, Bo; Zou, Yuru
2018
Eigentime identity of the weighted Koch networks. Zbl 1433.34043
Sun, Yu; Zou, Jiahui; Dai, Meifeng; Wang, Xiaoqian; Tang, Hualong; Su, Weiyi
2018
Bounds on the support of the multifractal spectrum of stochastic processes. Zbl 1433.28014
Grahovac, Danijel; Leonenko, Nikolai N.
2018
Comparison principles for Hadamard-type fractional differential equations. Zbl 1433.34016
Yin, Chuntao; Ma, Li; Li, Changpin
2018
Affine Maurer-Cartan invariants and their applications in self-affine fractals. Zbl 1433.28035
Yang, Yun; Yu, Yanhua
2018
Markov spectra of self-similar networks by substitution rule. Zbl 1433.35441
Li, Tingting; Ye, Qianqian; Xi, Lifeng
2018
Hausdorff dimension of the exceptional sets concerning the run-length function of beta-expansion. Zbl 1433.11099
Zhang, Mengjie
2018
Iterated function systems with place-dependent probabilities and the inverse problem of measure approximation using moments. Zbl 1433.37021
La Torre, D.; Maki, E.; Mendivil, F.; Vrscay, E. R.
2018
Fractal approximation of Jackson type for periodic phenomena. Zbl 1433.28023
Navascués, M. A.; Jha, Sangita; Chand, A. K. B.; Sebastián, M. V.
2018
On Hadamard fractional calculus. Zbl 1371.26009
Ma, Li; Li, Changpin
2017
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
Average geodesic distance of Sierpinski gasket and Sierpinski networks. Zbl 1375.28020
Wang, Songjing; Yu, Zhouyu; Xi, Lifeng
2017
Dimension analysis of continuous functions with unbounded variation. Zbl 1371.28012
Wang, Jun; Yao, Kui
2017
Fractal dimension of certain continuous functions of unbounded variation. Zbl 1371.28005
Liang, Y. S.; Su, W. Y.
2017
Average geodesic distance of Sierpinski carpet. Zbl 1432.28015
Zhao, Luming; Wang, Songjing; Xi, Lifeng
2017
Construction and analysis of a special one-dimensional continuous function. Zbl 1371.28011
Wang, J.; Yao, Kui
2017
Assouad-minimality of Moran sets under quasi-Lipschitz mappings. Zbl 1371.28013
Xi, Lifeng; Deng, Juan; Wen, Zhiying
2017
A new nonlinear fractal interpolation function. Zbl 1432.41001
Ri, Songil
2017
Fractional calculus of coalescence hidden-variable fractal interpolation functions. Zbl 1371.28026
2017
On the topological classification of fractal squares. Zbl 1371.28027
Rao, Feng; Wang, Xiaohua; Wen, Shengyou
2017
Definition and classification of one-dimensional continuous functions with unbounded variation. Zbl 1375.28010
Liang, Y. S.
2017
Random walks with a trap in scale-free fractal hierarchical lattices. Zbl 1432.05104
Xing, Changming; Yang, Lin; Guo, Lei
2017
Answers to questions on Ćirić type theorems. Zbl 06785046
Nguyen Van Dung
2017
Quasi-lower dimension and quasi-Lipschitz mapping. Zbl 1371.28003
Chen, Haipeng; Du, Yali; Wei, Chun
2017
Box dimension of Hadamard fractional integral of continuous functions of bounded and unbounded variation. Zbl 1371.26012
Wu, Xiao Er; Du, Jun Huai
2017
Box-counting dimension computed by {$$\alpha$$}-dense curves. Zbl 1375.28009
García, G.; Mora, G.; Redtwitz, D. A.
2017
The Cantor set’s multi-fractal spectrum formed by different probability factors in mathematical experiment. Zbl 1371.28009
Pan, Xuezai; Shang, Xudong; Wang, Minggang; Zuo-Fei
2017
Tricomplex dynamical systems generated by polynomials of odd degree. Zbl 1371.28025
Parisé, Pierre-Olivier; Rochon, Dominic
2017
More about Cantor like sets in hyperbolic numbers. Zbl 1375.28019
Téllez-Sánchez, Gamaliel Yafte; Bory-Reyes, Juan
2017
Self-similar subsets of symmetric Cantor sets. Zbl 1371.28032
Zeng, Ying
2017
A preliminary study on the fractal phenomenon: “Disconnected + disconnected=connected”. Zbl 1371.28031
Wang, Da; Liu, Shutang; Zhao, Yang
2017
The generalization of Sierpinski carpet and Menger Sponge in $$n$$-dimensional space. Zbl 1375.28021
Yang, Yun; Feng, Yuting; Yu, Yanhua
2017
Fractal dimension of Riemann-Liouville fractional integral of certain unbounded variational continuous function. Zbl 1375.28016
Li, Yang; Xiao, Wei
2017
The exceptional sets on the run-length function of $$\beta$$-expansions. Zbl 1432.11104
Zheng, Lixuan; Wu, Min; Li, Bing
2017
Box dimensions of {$$\alpha$$}-fractal functions. Zbl 1354.28002
Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A.
2016
Horton law in self-similar trees. Zbl 1351.28014
Kovchegov, Yevgeniy; Zaliapin, Ilya
2016
Fractal trigonometric polynomials for restricted range approximation. Zbl 1351.28009
Chand, A. K. B.; Navascués, M. A.; Viswanathan, P.; Katiyar, S. K.
2016
Remarks on dimensions of Cartesian product sets. Zbl 1354.28003
Wei, Chun; Wen, Shengyou; Wen, Zhixiong
2016
Cantor-type sets in hyperbolic numbers. Zbl 1357.28008
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016
Scale-free and small-world properties of VAF fractal networks. Zbl 1354.28006
Li, Hao; Huang, Jian; Le, Anbo; Wang, Qin; Xi, Lifeng
2016
A small-world and scale-free network generated by Sierpinski tetrahedron. Zbl 1342.28012
Chen, Jin; Gao, Fei; Le, Anbo; Xi, Lifeng; Yin, Shuhua
2016
A new class of fractal interpolation surfaces based on functional values. Zbl 1343.65010
Chand, A. K. B.; Vijender, N.
2016
A type of fractal interpolation functions and their fractional calculus. Zbl 1351.28016
Liang, Yong-Shun; Zhang, Qi
2016
Partially blended constrained rational cubic trigonometric fractal interpolation surfaces. Zbl 1354.28004
Chand, A. K. B.; Tyada, K. R.
2016
Langevin equation on fractal curves. Zbl 1354.28008
Satin, Seema; Gangal, A. D.
2016
Separable local fractional differential equations. Zbl 1355.34017
Kolwankar, Kiran M.
2016
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#### Cited by 2,566 Authors

 36 Chand, Arya Kumar Bedabrata 28 Navascués, María Antonia 26 Viswanathan, Puthan Veedu 23 Su, Weiyi 22 Wang, Xingyuan 18 Xi, Lifeng 16 Strichartz, Robert S. 16 Taqqu, Murad S. 14 Băleanu, Dumitru I. 13 Vijender, Nallapu 11 Dai, Meifeng 11 Golmankhaneh, Alireza Khalili 11 Liu, Fawang 11 Rochon, Dominic 11 Yao, Kui 10 El-Nabulsi, Rami Ahmad 10 Fraser, Jonathan MacDonald 10 Loridant, Benoit 10 Ma, Chunsheng 10 Teplyaev, Alexander 9 Didier, Gustavo 9 Drakopoulos, Vasileios 9 Leonenko, Nikolai N. 9 Ngai, Sze-Man 9 Thuswaldner, Jörg Maximilian 8 Anh, Vo V. 8 Bárány, Balázs 8 Bardet, Jean-Marc 8 Bouboulis, Pantelis 8 Dalla, Leoni 8 Gorenflo, Rudolf 8 Liang, Yongshun 8 Machado, José António Tenreiro 8 Mainardi, Francesco 8 Meerschaert, Mark Marvin 8 Telesca, Luciano 7 Arneodo, Alain 7 Falconer, Kenneth J. 7 Hilfer, Rudolf 7 Jørgensen, Palle E. T. 7 Katiyar, Saurabh Kumar 7 Kovchegov, Yevgeniy V. 7 Lévy Véhel, Jacques 7 Montoya, Fausto 7 Pastor, Gerardo 7 Prasad, M. Guru Prem 7 Romera, Miguel 7 Stanley, H. Eugene 7 Stenflo, Orjan 7 Turner, Ian William 7 Wang, Qin 7 Wu, Bo 7 Yu, Boming 6 Balankin, Alexander S. 6 Jiang, Kan 6 Ju, Tingting 6 Käenmäki, Antti 6 Li, Changpin 6 Li, Wenxia 6 Luo, Jun 6 Qiu, Hua 6 Sandev, Trifce 6 Saxena, Ram Kishore 6 Shahverdian, Ashot Yu. 6 Sun, Yu 6 Vâjiac, Adrian I. 6 Xue, Yumei 6 Yang, Xiao-Jun 6 Zaliapin, Ilya 6 Zhou, Songping 5 Akhtar, Md. Nasim 5 Akiyama, Shigeki 5 Berg, Kimmo 5 Bory Reyes, Juan 5 Chen, Yangquan 5 Gangal, Anil D. 5 Gdawiec, Krzysztof 5 Gu, Jiangwen 5 Haq, Sirajul 5 Hussain, Manzoor 5 Kapoor, Govind P. 5 Lau, Kasing 5 Li, Ming 5 Li, Yin 5 Lu, Jian 5 Luchko, Yuri 5 Miculescu, Radu 5 Morris, Ian D. 5 Orúe, Amalia B. 5 Ri, Songil 5 Ruan, Huo-Jun 5 Satin, Seema E. 5 Schertzer, Daniel 5 Sebastián, María Victoria 5 Sirvent, Víctor F. 5 Steinhurst, Benjamin 5 Sun, Yuanyuan 5 Wen, Shengyou 5 Xu, Xiaojie 5 Ye, Qianqian ...and 2,466 more Authors
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#### Cited in 387 Journals

 227 Fractals 91 Chaos, Solitons and Fractals 46 Journal of Mathematical Analysis and Applications 42 Physica A 41 Applied Mathematics and Computation 33 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 30 Journal of Statistical Physics 29 Chaos 28 Nonlinear Dynamics 24 Computers & Mathematics with Applications 24 Fractional Calculus & Applied Analysis 22 Communications in Nonlinear Science and Numerical Simulation 19 Journal of Mathematical Physics 18 Physica D 18 Mathematical Problems in Engineering 18 Journal of Statistical Mechanics: Theory and Experiment 16 Abstract and Applied Analysis 15 Physics Letters. A 14 Journal of Computational and Applied Mathematics 14 Stochastic Processes and their Applications 13 Statistics & Probability Letters 13 Discrete Dynamics in Nature and Society 12 Mediterranean Journal of Mathematics 10 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 10 Transactions of the American Mathematical Society 10 Ergodic Theory and Dynamical Systems 10 Advances in Applied Clifford Algebras 10 Bernoulli 10 International Journal of Modern Physics C 10 Journal of Applied Mathematics and Computing 9 Journal of Computational Physics 9 Advances in Mathematics 9 Proceedings of the American Mathematical Society 9 Journal of Mathematics 8 International Journal of Computer Mathematics 8 Computational Statistics and Data Analysis 8 Advances in Difference Equations 7 International Journal of Heat and Mass Transfer 7 Results in Mathematics 7 Stochastic Analysis and Applications 7 Acta Applicandae Mathematicae 7 Journal of Theoretical Probability 7 Applied Mathematics Letters 7 Mathematical and Computer Modelling 7 Applied Mathematical Modelling 7 Journal of Statistical Computation and Simulation 7 Computational and Applied Mathematics 7 Complexity 7 The Journal of Fourier Analysis and Applications 7 Entropy 7 The European Physical Journal B. Condensed Matter and Complex Systems 6 Nonlinearity 6 Journal of Multivariate Analysis 6 Mathematische Nachrichten 6 Monatshefte für Mathematik 6 Theoretical Computer Science 6 Quantitative Finance 6 Journal of Theoretical Biology 6 Journal of Fractal Geometry 5 International Journal of Modern Physics B 5 Bulletin of the Australian Mathematical Society 5 Communications in Mathematical Physics 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 Journal of Time Series Analysis 5 Applied Numerical Mathematics 5 Numerical Algorithms 5 Communications in Statistics. Simulation and Computation 5 Indagationes Mathematicae. New Series 5 Experimental Mathematics 5 Applied Mathematics. Series B (English Edition) 5 International Journal of Theoretical and Applied Finance 5 Advances in Mathematical Physics 5 Statistics and Computing 5 Mathematics 4 Acta Mechanica 4 Advances in Applied Probability 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 Mathematics and Computers in Simulation 4 Mathematische Zeitschrift 4 Topology and its Applications 4 Journal of Scientific Computing 4 Applied and Computational Harmonic Analysis 4 Discrete and Continuous Dynamical Systems 4 Journal of Applied Statistics 4 Statistical Inference for Stochastic Processes 4 Acta Mathematica Sinica. English Series 4 Journal of Applied Mathematics 4 Analysis in Theory and Applications 4 Fixed Point Theory and Applications 3 Applicable Analysis 3 Classical and Quantum Gravity 3 General Relativity and Gravitation ...and 287 more Journals
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#### Cited in 61 Fields

 606 Measure and integration (28-XX) 258 Dynamical systems and ergodic theory (37-XX) 258 Probability theory and stochastic processes (60-XX) 196 Real functions (26-XX) 196 Numerical analysis (65-XX) 184 Partial differential equations (35-XX) 170 Statistics (62-XX) 123 Ordinary differential equations (34-XX) 115 Statistical mechanics, structure of matter (82-XX) 92 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 89 Biology and other natural sciences (92-XX) 83 Approximations and expansions (41-XX) 72 Computer science (68-XX) 69 Information and communication theory, circuits (94-XX) 67 Harmonic analysis on Euclidean spaces (42-XX) 62 Fluid mechanics (76-XX) 61 Combinatorics (05-XX) 49 Number theory (11-XX) 48 Operator theory (47-XX) 36 Functions of a complex variable (30-XX) 35 Special functions (33-XX) 34 General topology (54-XX) 34 Mechanics of deformable solids (74-XX) 34 Operations research, mathematical programming (90-XX) 33 Quantum theory (81-XX) 31 Geophysics (86-XX) 30 Convex and discrete geometry (52-XX) 27 Functional analysis (46-XX) 24 Potential theory (31-XX) 24 Systems theory; control (93-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 16 Integral transforms, operational calculus (44-XX) 16 Integral equations (45-XX) 16 Mechanics of particles and systems (70-XX) 16 Classical thermodynamics, heat transfer (80-XX) 15 Relativity and gravitational theory (83-XX) 14 Global analysis, analysis on manifolds (58-XX) 12 Difference and functional equations (39-XX) 12 Differential geometry (53-XX) 9 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) 8 Optics, electromagnetic theory (78-XX) 7 Group theory and generalizations (20-XX) 7 Geometry (51-XX) 6 Topological groups, Lie groups (22-XX) 6 Abstract harmonic analysis (43-XX) 6 Astronomy and astrophysics (85-XX) 4 Mathematical logic and foundations (03-XX) 4 Algebraic geometry (14-XX) 4 Mathematics education (97-XX) 3 History and biography (01-XX) 3 Algebraic topology (55-XX) 3 Manifolds and cell complexes (57-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 General algebraic systems (08-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Sequences, series, summability (40-XX)