## Fractals

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

 Short Title: Fractals Publisher: World Scientific, Singapore ISSN: 0218-348X; 1793-6543/e Online: https://www.worldscientific.com/loi/fractals
 Documents Indexed: 1,260 Publications (since 1993) References Indexed: 984 Publications with 25,570 References.
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### Authors

 26 Xi, Lifeng 16 Băleanu, Dumitru I. 15 Chu, Yuming 14 Abdeljawad, Thabet 13 Shah, Kamal 13 Yu, Boming 12 Chand, Arya Kumar Bedabrata 11 Dai, Meifeng 11 Gómez-Aguilar, José Francisco 11 Su, Weiyi 11 Wang, Xingyuan 10 Havlin, Shlomo 10 Taqqu, Murad S. 10 Wang, Kangle 10 Wang, Qin 10 Xiao, Boqi 9 Giona, Massimiliano 9 Karaca, Yeliz 9 Rashid, Saima 9 Stanley, H. 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
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### 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)

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579 Publications have been cited 2,766 times in 1,982 Documents Cited by Year
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The relationship between fractional calculus and fractals. Zbl 0877.28009
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Distributed order fractional sub-diffusion. Zbl 1083.60066
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Bivariate fractal interpolation functions on grids. Zbl 1088.28502
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The study of bivariate fractal interpolation functions and creation of fractal interpolated surfaces. Zbl 0908.65005
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Hidden variable bivariate fractal interpolation surfaces. Zbl 1046.28004
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On the Riemann-Liouville fractional calculus and some recent applications. Zbl 0868.26004
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Calculus on fractal subsets of real line. I: Formulation. Zbl 1173.28005
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A generalized Mandelbrot set for bicomplex numbers. Zbl 0969.37021
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On Hadamard fractional calculus. Zbl 1371.26009
Ma, Li; Li, Changpin
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Dimensions of self-affine fractals and multifractals generated by upper-triangular matrices. Zbl 1137.28302
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2007
Simulation methods for linear fractional stable motion and FARIMA using the fast Fourier transform. Zbl 1083.65005
2004
Cooperative strategies in formation of complex bacterial patterns. Zbl 0869.92002
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1995
A fractal valued random iteration algorithm and fractal hierarchy. Zbl 1304.28004
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2005
On fractional relaxation. Zbl 1140.82315
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Fractal bases of $$L_p$$ spaces. Zbl 1251.28009
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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
Multifractal cascade dynamics and turbulent intermittency. Zbl 0927.76044
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Average geodesic distance of Sierpinski gasket and Sierpinski networks. Zbl 1375.28020
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2017
Topological structure of self-similar sets. Zbl 1075.28005
Luo, Jun; Rao, Hui; Tan, Bo
2002
Hidden variable vector valued fractal interpolation functions. Zbl 1100.41011
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2005
Analysis of fractional differential equations with multi-orders. Zbl 1176.34008
Deng, Weihua; Li, Changpin; Guo, Qian
2007
On the dimension of self-similar sets. Zbl 1088.28504
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2002
Modifications at large distances from fractional and fractal arguments. Zbl 1196.28014
2010
Exact solutions for a class of fractal time random walks. Zbl 0881.60066
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Analysis of $$\mathbb{C}$$-plane fractal images from $$z \leftarrow z^{\alpha} + c$$ for $$(\alpha < 0)$$. Zbl 1211.37059
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2000
Foundations of fractional dynamics. Zbl 0870.58041
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Certain integral inequalities considering generalized $$m$$-convexity on fractal sets and their applications. Zbl 1434.28018
2019
Vibration spectra of finitely ramifield, symmetric fractals. Zbl 1160.28302
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2008
Central limit theorem for the log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context. Zbl 1141.62073
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2007
Fractal image compression. Zbl 0903.68211
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1994
Nonextensive thermostatics and fractals. Zbl 0870.58098
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1995
On a generalized Fatou-Julia theorem in multicomplex spaces. Zbl 1177.30068
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2009
Normal families of bicomplex holomorphic functions. Zbl 1230.30032
Charak, K. S.; Rochon, D.; Sharma, N.
2009
Box dimensions of {$$\alpha$$}-fractal functions. Zbl 1354.28002
Akhtar, Md. Nasim; Prasad, M. Guru Prem; Navascués, M. A.
2016
Estimation and simulation of fractal stochastic point processes. Zbl 0881.60044
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1995
Path properties of the linear multifractional stable motion. Zbl 1304.28010
2005
On stability of fractal interpolation. Zbl 0974.28003
Feng, Zhigang; Xie, Heping
1998
Calculus on fractal curves in $$\mathbb{R}^{n}$$. Zbl 1217.28014
Parvate, Abhay; Satin, Seema; Gangal, A. D.
2011
Calculus on fractal subsets of real line. II: Conjugacy with ordinary calculus. Zbl 1252.28005
Parvate, Abhay; Gangal, A. D.
2011
Analysis, synthesis, and estimation of fractal-rate stochastic point processes. Zbl 0907.62093
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1997
A technique in the topology of connected self-similar tiles. Zbl 1304.28009
Ngai, Sze-Man; Tang, Tai-Man
2004
Dimension analysis of continuous functions with unbounded variation. Zbl 1371.28012
Wang, Jun; Yao, Kui
2017
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
On a generalized Fatou-Julia theorem. Zbl 1041.37023
Rochon, Dominic
2003
Fractal geometry of financial time series. Zbl 0869.62073
Evertsz, Carl J. G.
1995
Average geodesic distance of Sierpinski carpet. Zbl 1432.28015
Zhao, Luming; Wang, Songjing; Xi, Lifeng
2017
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
2003
$$1/f$$ 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
Vector random fields with long-range dependence. Zbl 1232.60038
Ma, Chunsheng
2011
Fractal interpolation functions on post critically finite self-similar sets. Zbl 1196.28019
Ruan, Huo-Jun
2010
Generalizations of Newton’s method. Zbl 1046.37027
Gilbert, William J.
2001
Fractal modeling of speech signals. Zbl 1126.94308
Lévy Véhel, Jacques; Daoudi, Khalid; Lutton, Evelyne
1994
An analysis of U.S. stock price behavior using wavelets. Zbl 0877.90027
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1995
On smoothness for a class of fractal interpolation surfaces. Zbl 1302.37020
Wang, Hong-Yong
2006
Average distance of self-similar fractal trees. Zbl 1432.28007
Li, Tingting; Jiang, Kan; Xi, Lifeng
2018
Study on the fractal and chaotic features of the Shanghai composite index. Zbl 1250.91084
Wen, Fenghua; Li, Zhong; Xie, Chaohua; Shaw, David
2012
On the Assouad dimension of graph directed Moran fractals. Zbl 1222.28017
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2011
Cantor-type sets in hyperbolic numbers. Zbl 1357.28008
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016
The multifractal dimension functions of homogeneous Moran measure. Zbl 1165.28005
Xiao, Jiaqing; Wu, Min
2008
Some results of convergence of cubic spline fractal interpolation functions. Zbl 1053.41013
Navascués, M. Antonia; Sebastián, M. Victoria
2003
Fractal description of anomalous diffusion in dynamical systems. Zbl 0901.58050
Klafter, J.; Zumofen, G.; Shlesinger, M. F.
1993
The fractal dimension of the Apollonian sphere packing. Zbl 0908.52008
Borkovec, M.; de Paris, W.; Peikert, R.
1994
Fractal approaches in signal processing. Zbl 0867.94005
Lévy-Véhel, Jacques
1995
Lipschitz equivalence of McMullen sets. Zbl 1290.28012
Li, Boming; Li, Wenxia; Miao, Jun Jie
2013
On the automatic selection of the onset of scaling. Zbl 1056.62102
Veitch, Darryl; Abry, Patrice; Taqqu, Murad S.
2003
The Hosoya index of graphs formed by a fractal graph. Zbl 1434.05039
Liu, Jia-bao; Zhao, Jing; Min, Jie; Cao, Jinde
2019
Natural cubic spline coalescence hidden variable fractal interpolation surfaces. Zbl 1250.28004
Chand, A. K. B.
2012
Fractal dimension of certain continuous functions of unbounded variation. Zbl 1371.28005
Liang, Y. S.; Su, W. Y.
2017
Multifractal cross-correlation analysis based on statistical moments. Zbl 1272.28013
Wang, Jing; Shang, Pengjian; Ge, Weijie
2012
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
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
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
Rényi function for multifractal random fields. Zbl 1278.28003
Leonenko, Nikolai N.; Shieh, Narn-Rueih
2013
An user intention mining model based on fractal time series pattern. Zbl 07468599
Wu, Shaofei
2020
A remark on Wang’s fractal variational principle. Zbl 1434.35267
Wang, Kang-Le; He, Chun-Hui
2019
K-iterated function system. Zbl 1190.28004
Sahu, D. R.; Chakraborty, Anindita; Dubey, R. P.
2010
When Thue-Morse meets Koch. Zbl 1110.28007
Ma, Jun; Holdener, Judy
2005
Lipschitz equivalence of general Sierpinski carpets. Zbl 1159.28004
Dai, Meifeng
2008
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
Hausdorff measure of Cartesian product of the ternary Cantor set. Zbl 1243.28003
Deng, Juan; Rao, Hui; Wen, Zhi-Ying
2012
The boundary of the attractor of a recurrent iterated function system. Zbl 1088.28503
Dekking, F. M.; van der Wal, P.
2002
A new nonlinear fractal interpolation function. Zbl 1432.41001
Ri, Songil
2017
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
Construction and analysis of a special one-dimensional continuous function. Zbl 1371.28011
Wang, J.; Yao, Kui
2017
The quasi-sine Fibonacci hyperbolic dynamic system. Zbl 1192.37066
Wang, Xing-Yuan; Ge, Feng-Dan
2010
Remarks on dimensions of Cartesian product sets. Zbl 1354.28003
Wei, Chun; Wen, Shengyou; Wen, Zhixiong
2016
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
Composed accelerated escape time algorithm to construct the general Mandelbrot sets. Zbl 1046.37030
Liu, Xiangdong; Zhu, Zhiliang; Wang, Guangxing; Zhu, Weiyong
2001
On Lévy stable and semistable distributions. Zbl 1045.60010
Huillet, Thierry; Porzio, Anna; Alaya, Mohamed Ben
2001
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
Some further extensions considering discrete proportional fractional operators. Zbl 07490662
Rashid, Saima; Sultana, Sobia; Karaca, Yeliz; Khalid, Aasma; Chu, Yu-Ming
2022
Jensen-Mercer inequality and related results in the fractal sense with applications. Zbl 07490644
2022
Caputo type fractional operator applied to hepatitis B system. Zbl 07490659
Din, Anwarud; Li, Yongjin; Yusuf, Abdullahi; Ali, Aliyu Isa
2022
Impact of the same degenerate additive noise on a coupled system of fractional space diffusion equations. Zbl 07490669
Mohammed, Wael W.; Iqbal, Naveed
2022
Shifted Legendre fractional pseudospectral differentiation matrices for solving fractional differential problems. Zbl 07490674
Abdelhakem, Mohamed; Abdelhamied, Dina; Alshehri, Maryam G.; El-Kady, Mamdouh
2022
Variational principle and approximate solution for the generalized Burgers-Huxley equation with fractal derivative. Zbl 1482.35008
Wang, Kang-Jia
2021
Optimal control of nonlinear time-delay fractional differential equations with Dickson polynomials. Zbl 1481.49032
Chen, Shu-Bo; Soradi-Zeid, Samaneh; Alipour, Maryam; Chu, Yu-Ming; Gómez-Aguilar, J. F.; Jahanshahi, Hadi
2021
Infinite number of parameter regions with fractal nonchaotic attractors in a piecewise map. Zbl 07465590
Cheng, Tao; Zhang, Yongxiang; Shen, Yunzhu
2021
Strange nonchaotic attractors and multistability in a two-degree-of-freedom quasiperiodically forced vibro-impact system. Zbl 07465605
Li, Gaolei; Yue, Yuan; Grebogi, Celso; Li, Denghui; Xie, Jianhua
2021
Solvability of the Moore-Gibson-Thompson equation with viscoelastic memory term and integral condition via Galerkin method. Zbl 1482.35238
Boulaaras, Salah
2021
Stability result and well-posedness for Timoshenko’s beam laminated with thermoelastic and past history. Zbl 1482.35040
Choucha, Abdelbaki; Boulaaras, Salah; Ouchenane, Djamel; Alkhalaf, Salem; Cherif, Bahri
2021
Analysis of mixed Weyl-Marchaud fractional derivative and box dimensions. Zbl 07467682
Chandra, Subhash; Abbas, Syed
2021
Computational modeling and theoretical analysis of nonlinear fractional order prey-predator system. Zbl 07465334
Ali, Amjad; Shah, Kamal; Alrabaiah, Hussam; Shah, Zahir; Ur Rahman, Ghaus; Islam, Saeed
2021
A fractal-Monte Carlo approach to model oil and water two-phase seepage in low-permeability reservoirs with rough surfaces. Zbl 07465336
Su, Haibo; Zhang, Yidan; Xiao, Boqi; Huang, Xiaoming; Yu, Boming
2021
Maclaurin series method for fractal differential-difference models arising in coupled nonlinear optical waveguides. Zbl 1481.78012
Khan, Yasir
2021
Extensions of the Shannon entropy and the chaos game algorithm to hyperbolic numbers plane. Zbl 07465346
Téllez-Sánchez, G. Y.; Bory-Reyes, J.
2021
A fractal model for capillary flow through a single tortuous capillary with roughened surfaces in fibrous porous media. Zbl 07465350
Xiao, Boqi; Huang, Qiwen; Chen, Hanxin; Chen, Xubing; Long, Gongbo
2021
On the fractal variational principle for the telegraph equation. Zbl 1482.35005
He, Ji-Huan
2021
Bifurcations emerging from different delays in a fractional-order predator-prey model. Zbl 07465379
Huang, Chengdai; Li, Huan; Chen, Xiaoping; Cao, Jinde
2021
Stability analysis of nonlinear uncertain fractional differential equations with Caputo derivative. Zbl 07465400
Lu, Ziqiang; Zhu, Yuanguo; Lu, Qinyun
2021
The calculus of bivariate fractal interpolation surfaces. Zbl 07465408
Chandra, Subhash; Abbas, Syed
2021
A fractal model for predicting oxygen effective diffusivity of porous media with rough surfaces under dry and wet conditions. Zbl 07465418
Xiao, Boqi; Huang, Qiwen; Yu, Boming; Long, Gongbo; Chen, Hanxin
2021
Generalized synchronization and parameters identification of different-dimensional chaotic systems in the complex field. Zbl 1481.93061
Liu, Jian; Chen, Guanrong; Zhao, Xiu
2021
A novel perspective for the fractal Schrödinger equation. Zbl 1482.35011
Wang, Kang-Le
2021
Finite-time stability in mean for nabla uncertain fractional order linear difference systems. Zbl 1481.39007
Lu, Qinyun; Zhu, Yuanguo; Li, Bo
2021
On the largest partial quotients in continued fraction expansions. Zbl 1483.11159
Fang, Lulu; Liu, Jian
2021
On the approximate solutions for a system of coupled Korteweg-de Vries equations with local fractional derivative. Zbl 07465612
Jafari, Hossein; Jassim, Hassan Kamil; Baleanu, Dumitru; Chu, Yu-Ming
2021
Complex fractional-order HIV diffusion model based on amplitude equations with Turing patterns and Turing instability. Zbl 1481.92036
Iqbal, Naveed; Karaca, Yeliz
2021
Solution of the local fractional generalized KdV equation using homotopy analysis method. Zbl 1482.35064
Jafari, Hossein; Prasad, Jyoti Geetesh; Goswami, Pranay; Dubey, Ravi Shanker
2021
Existence results for ABC-fractional differential equations with non-separated and integral type of boundary conditions. Zbl 07465616
Mehmood, Nayyar; Abbas, Ahsan; Abdeljawad, Thabet; Akgül, Ali
2021
Fractional Mayer neuro-swarm heuristic solver for multi-fractional order doubly singular model based on Lane-Emden equation. Zbl 1481.65104
Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru
2021
New multi-functional approach for $$\kappa$$th-order differentiability governed by fractional calculus via approximately generalized $$(\psi, \hbar)$$-convex functions in Hilbert space. Zbl 07465619
Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-Ming
2021
Design of neuro-swarming heuristic solver for multi-pantograph singular delay differential equation. Zbl 1481.65098
Sabir, Zulqurnain; Baleanu, Dumitru; Raja, Muhammad Asif Zahoor; Guirao, Juan L. G.
2021
A powerful iterative approach for quintic complex Ginzburg-Landau equation within the frame of fractional operator. Zbl 07465623
Yao, Shao-Wen; Ilhan, Esin; Veeresha, P.; Baskonus, Haci Mehmet
2021
New computations of Ostrowski-type inequality pertaining to fractal style with applications. Zbl 07465626
Al Qurashi, Maysaa; Rashid, Saima; Khalid, Aasma; Karaca, Yeliz; Chu, Yu-Ming
2021
Achieving more precise bounds based on double and triple integral as proposed by generalized proportional fractional operators in the Hilfer sense. Zbl 1481.26004
Al-Qurashi, Maysaa; Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming
2021
Monotonicity and asymptotic properties of solutions for parabolic equations via a given initial value condition on graphs. Zbl 1482.35058
Wu, Yiting
2021
Study of nonlinear Hirota-Satsuma coupled KdV and coupled mKdV system with time fractional derivative. Zbl 07465629
2021
Combined electroosmotic and pressure driven flow in tree-like microchannel network. Zbl 07465631
Liu, Fei; Jing, Dalei
2021
A fractal model for predicting the effective thermal conductivity of roughened porous media with microscale effect. Zbl 1481.80008
Xiao, Boqi; Zhang, Min; Chen, Hanxin; Cao, Jiyin; Long, Gongbo; Zhao, Zheng
2021
Low frequency property of a fractal vibration model for a concrete beam. Zbl 1482.74083
He, Chun-Hui; Liu, Chao; He, Ji-Huan; Gepreel, Khaled A.
2021
A new perspective on the study of the fractal coupled Boussinesq-Burger equation in shallow water. Zbl 07465643
Wang, Kang-Jia; Wang, Guo-Dong; Zhu, Hong-Wei
2021
The difference between the Hurwitz continued fraction expansions of a complex number and its rational approximations. Zbl 1483.11146
He, Yubin; Xiong, Ying
2021
Analysis on Weyl-Marchaud fractional derivative for types of fractal interpolation function with fractal dimension. Zbl 07468100
Priyanka, T. M. C.; Gowrisankar, A.
2021
An investigation on spontaneous imbibition in tree-like branching network with fractal roughened surfaces. Zbl 1482.80005
Xiao, Boqi; Liu, Zhenjie; Zhang, Yidan; Liang, Mingchao; Long, Gongbo; Zhao, Zheng
2021
Fractal propagation and immunity on network. Zbl 1481.92153
Nian, Fuzhong; Yang, Yang; Shi, Yayong
2021
A comparative study of semi-analytical methods for solving fractional-order Cauchy reaction-diffusion equation. Zbl 07467680
Chu, Yu-Ming; Shah, Nehad Ali; Ahmad, Hijaz; Chung, Jae Dong; Khaled, S. M.
2021
A fractal model for effective thermal conductivity of dual-porosity media with randomly distributed tree-like networks. Zbl 1482.80006
Zhang, Jun; Wang, Yizhi; Lou, Gang; Kou, Jianlong
2021
A novel model for effective thermal conductivity of tree-like branching network with fractal roughened surfaces. Zbl 1482.80003
Liu, Yonghui; Li, Zihao; Xiao, Boqi; Chen, Hanxin; Long, Gongbo
2021
An user intention mining model based on fractal time series pattern. Zbl 07468599
Wu, Shaofei
2020
Newton’s-type integral inequalities via local fractional integrals. Zbl 1434.26052
Iftikhar, Sabah; Kumam, Poom; Erden, Samet
2020
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
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
Lower Assouad-type dimensions of uniformly perfect sets in doubling metric spaces. Zbl 1434.28014
Chen, Haipeng; Wu, Min; Chang, Yuanyang
2020
Variational principle for a generalized KdV equation in a fractal space. Zbl 1441.35009
Shen, Yue; He, Ji-Huan
2020
Fractal networks on Sierpinski-type polygon. Zbl 1445.28019
Zeng, Cheng; Xue, Yumei; Zhou, Meng
2020
On the weighted fractional operators of a function with respect to another function. Zbl 07468593
2020
New estimates of integral inequalities via generalized proportional fractional integral operator with respect to another function. Zbl 07468609
Rashid, Saima; Hammouch, Zakia; Jarad, Fahd; Chu, Yu-Ming
2020
Generalized $$h$$-convexity on fractal sets and some generalized Hadamard-type inequalities. Zbl 1434.28036
Sun, Wenbing
2020
The average weighted path length for a class of hierarchical networks. Zbl 1441.05208
Niu, Min; Li, Ruixia
2020
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
2020
A lower bound of topological Hausdorff dimension of fractal squares. Zbl 1445.28021
Zhang, Yan-Fang
2020
New generalizations in the sense of the weighted non-singular fractional integral operator. Zbl 07468585
Rashid, Saima; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming
2020
Mathematical analysis of coupled systems with fractional order boundary conditions. Zbl 07468594
Ali, Zeeshan; Shah, Kamal; Zada, Akbar; Kumam, Poom
2020
Qualitative study of nonlinear coupled pantograph differential equations of fractional order. Zbl 07468627
2020
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
2020
Fractal Stokes’ theorem based on integrals on fractal manifolds. Zbl 1434.28009
Wu, Junru; Wang, Chengyuan
2020
Wada fractal basins of attraction in a zero-stiffness vibration isolation system. Zbl 1434.28044
Zhang, Fanhui; Zhang, Yongxiang
2020
Construction of fractal surfaces. Zbl 1434.28031
Navascués, M. A.; Mohapatra, R. N.; Akhtar, M. N.
2020
Average distances of a family of non-p.c.f. self-similar networks. Zbl 1434.05047
Zhao, Bing; Gu, Jiangwen; Xi, Lifeng
2020
Slow growth rate of the digits in Engel expansions. Zbl 1434.11155
Shang, Lei; Wu, Min
2020
The scale-free and small-world properties of complex networks on Sierpinski-type hexagon. Zbl 1434.28013
Cheng, Kun; Chen, Dirong; Xue, Yumei; Zhang, Qian
2020
Multiple exact solutions of the generalized time fractional foam drainage equation. Zbl 1441.34015
Shi, Dandan; Zhang, Yufeng; Liu, Wenhao
2020
Connectedness of a class of self-affine carpets. Zbl 1441.28009
Leung, King Shun; Luo, Jun Jason; Wang, Lian
2020
Mean value property of harmonic function on the higher-dimensional Sierpinski gasket. Zbl 1445.28016
Wu, Yipeng; Chen, Zhilong; Zhang, Xia; Zhao, Xudong
2020
Ahlfors-David regular subsets of fractals. Zbl 1445.28013
Pan, Yue; Xiong, Ying
2020
Box dimensions of the Riemann-Liouville fractional integral of Hölder continuous multivariate functions. Zbl 1445.26005
Lei, Jing; Liu, Kangjie; Dai, Yingzi
2020
Using a prior estimate method to investigate sequential hybrid fractional differential equations. Zbl 07468586
2020
Existence and stability analysis of solutions for fractional Langevin equation with nonlocal integral and anti-periodic-type boundary conditions. Zbl 07468588
Devi, Amita; Kumar, Anoop; Abdeljawad, Thabet; Khan, Aziz
2020
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
2020
Digital imaging based on fractal theory and its spatial dimensionality. Zbl 07468596
Tian, Yuan; Cui, Gaoyuan; Morris, Harry
2020
Applicability of topological degree theory to evolution equation with proportional delay. Zbl 07468610
Sher, Muhammad; Shah, Kamal; Chu, Yu-Ming; Khan, Rahmat Ali
2020
Mathematical and statistical analysis of RL and RC fractional-order circuits. Zbl 07468612
2020
A novel $$R/S$$ fractal analysis and wavelet entropy characterization approach for robust forecasting based on self-similar time series modeling. Zbl 1482.91200
Karaca, Yeliz; Baleanu, Dumitru
2020
On explicit wave solutions of the fractional nonlinear DSW system via the modified Khater method. Zbl 1482.76026
Yue, Chen; Lu, Dianchen; Khater, Mostafa M. A.; Abdel-Aty, Abdel-Haleem; Alharbi, W.; Attia, Raghda A. M.
2020
Existence of 3-weak solutions for a new class of an overdetermined system of fractional partial integro-differential equations. Zbl 1483.35312
Boulaaras, Salah; Guefaifia, Rafik; Alharbi, Asma; Cherif, Bahri
2020
Analysis of dengue fever outbreak by generalized fractional derivative. Zbl 07468620
Bosch, Paul; Gómez-Aguilar, J. F.; Rodríguez, José M.; Sigarreta, José M.
2020
The numerical treatment of nonlinear fractal-fractional 2D Emden-Fowler equation utilizing 2D Chelyshkov polynomials. Zbl 07468624
Hosseininia, M.; Heydari, M. H.; Avazzadeh, Z.
2020
Cauchy problems with fractal-fractional operators and applications to groundwater dynamics. Zbl 1483.35315
Atangana, Abdon; Doungmo Goufo, Emile Franc
2020
Atangana-Seda numerical scheme for labyrinth attractor with new differential and integral operators. Zbl 07468626
Atangana, Abdon; İğret Araz, Seda
2020
Applications of bi-framelet systems for solving fractional order differential equations. Zbl 1482.65107
2020
Small-world and scale-free properties of the $$n$$-dimensional Sierpinski cube networks. Zbl 1434.28043
Zeng, Cheng; Zhou, Meng; Xue, Yumei
2020
Some remarks on fractional integral of one-dimensional continuous functions. Zbl 1434.26018
Yao, Jia; Chen, Ying; Li, Junqiao; Wang, Bin
2020
A class of spectral Moran measures on $$\mathbb{R}$$. Zbl 1434.28002
Liu, Zong-Sheng; Dong, Xin-Han; Zhang, Peng-Fei
2020
Hausdorff dimensions of some exceptional sets in the first Ostrogradsky series. Zbl 1434.28020
Feng, Yan; Tan, Bo
2020
Hölder continuity and box dimension for the Weyl fractional integral. Zbl 1434.26016
Tian, Long
2020
The growth rate of the digits in the Lüroth expansions. Zbl 1441.11188
Lü, Meiying
2020
A general comparison principle for Caputo fractional-order ordinary differential equations. Zbl 1441.34018
Wu, Cong
2020
Dirichlet problem of Poisson equations and variational principle on a type of fractal sets. Zbl 1445.28017
Wu, Yipeng; Yao, Kui; Mu, Lei; Chen, Zhilong
2020
Family of shape preserving fractal-like Bézier curves. Zbl 1445.28014
Reddy, K. M.; Saravana Kumar, G.; Chand, A. K. B.
2020
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### 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
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### 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. A 15 Journal of Computational and Applied Mathematics 15 International Journal of Computer Mathematics 14 Stochastic Processes and their Applications 13 Statistics & Probability Letters 13 Discrete Dynamics in Nature and Society 12 Mediterranean Journal of Mathematics 12 AIMS 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 Results in Mathematics 9 Computational and Applied Mathematics 9 Journal of Mathematics 8 Applied Mathematics Letters 8 Journal of Statistical Computation and Simulation 8 Computational Statistics and Data Analysis 8 Journal of Fractal Geometry 7 International Journal of Heat and Mass Transfer 7 Stochastic Analysis and Applications 7 Acta Applicandae Mathematicae 7 Journal of Theoretical Probability 7 Mathematical and Computer Modelling 7 Applied Mathematical Modelling 7 Complexity 7 The Journal of Fourier Analysis and Applications 7 Entropy 7 The European Physical Journal B. Condensed Matter and Complex Systems 6 Acta Mechanica 6 Communications in Mathematical Physics 6 Nonlinearity 6 Journal of Multivariate Analysis 6 Mathematische Nachrichten 6 Monatshefte für Mathematik 6 Theoretical Computer Science 6 Applied Mathematics. Series B (English Edition) 6 Quantitative Finance 6 Boundary Value Problems 6 Journal of Theoretical Biology 5 International Journal of Modern Physics B 5 Bulletin of the Australian Mathematical Society 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 Mathematics and Computers in Simulation 5 Mathematische Zeitschrift 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 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
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### 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)