Results 21 to 30 of about 86,947 (328)
Analogues to Lie Method and Noether’s Theorem in Fractal Calculus
Fractal and Fractional, 2019 In this manuscript, we study symmetries of fractal differential equations. We show that using symmetry properties, one of the solutions can map to another solution.
Alireza Khalili Golmankhaneh +1 more
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The Maximum Entropy principle and the nature of fractals [PDF]
, 1998 We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in those patterns.
J Wagensberg +4 more
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Fractal and Fractional, 2019 In this paper, we give difference equations on fractal sets and their corresponding fractal differential equations. An analogue of the classical Euler method in fractal calculus is defined. This fractal Euler method presets a numerical method for solving
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source
Estimation of the Fractal Dimensions of the Linear Combination of Continuous Functions
Mathematics, 2022 In the present paper, we try to estimate the fractal dimensions of the linear combination of continuous functions with different fractal dimensions.
Binyan Yu, Yongshun Liang
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New Derivatives on the Fractal Subset of Real-Line
Entropy, 2016 In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets.
Alireza Khalili Golmankhaneh +1 more
doaj +1 more source
Correlated fractal percolation and the Palis conjecture [PDF]
, 2009 Let F1 and F2 be independent copies of correlated fractal percolation, with Hausdorff dimensions dimH(F1) and dimH(F2). Consider the following question: does dimH(F1)+dimH(F2)>1 imply that their algebraic difference F1-F2 will contain an interval?
B.B. Mandelbrot +6 more
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Advances in Difference Equations, 2021 The visual beauty reflects the practicability and superiority of design dependent on the fractal theory. Based on the applicability in practice, it shows that it is the completely feasible, self-comparability and multifaceted nature of fractal sets that ...
Yu-Ming Chu +4 more
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Some New Fractal Milne-Type Integral Inequalities via Generalized Convexity with Applications
Fractal and Fractional, 2023 This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set.
Badreddine Meftah +3 more
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Hermite-Hadamard-Fejér Inequalities for Preinvex Functions on Fractal Sets [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, for generalised preinvex functions, new estimates of the Fej\'{e}r-Hermite-Hadamard inequality on fractional sets $\mathbb{R}^{\rho }$ are given in this study.
Sikander Mehmood, Fiza Zafar
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Measuring Anisotropy in Planar Sets [PDF]
, 2018 We define and discuss a pure mathematics formulation of an approach proposed in the physics literature to analysing anisotropy of fractal ...
O'Neil, Toby C.
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