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Tsallis entropy on fractal sets
Journal of Taibah University for Science, 2021 In this article, we review fractal calculus ( $ F^{\alpha } $ -calculus) and define generalized Tsallis entropy on the fractal sets which is called fractal Tsallis entropy.
Alireza Khalili Golmankhaneh
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Fractal Schrödinger equation: implications for fractal sets [PDF]
Journal of Physics A: Mathematical and Theoretical, 2023 This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schrödinger equation and provides insights into its consequences.
A. Golmankhaneh +2 more
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Fractal Stochastic Processes on Thin Cantor-Like Sets
Mathematics, 2021 We review the basics of fractal calculus, define fractal Fourier transformation on thin Cantor-like sets and introduce fractal versions of Brownian motion and fractional Brownian motion. Fractional Brownian motion on thin Cantor-like sets is defined with
Alireza Khalili Golmankhaneh +1 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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Non-local Integrals and Derivatives on Fractal Sets with Applications [PDF]
Open Physics, 2016 In this paper, we discuss non-local derivatives on fractal Cantor sets. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared.
Golmankhaneh Alireza K., Baleanu D.
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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
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Diffusion on Middle-ξ Cantor Sets
Entropy, 2018 In this paper, we study Cζ-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions.
Alireza Khalili Golmankhaneh +3 more
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Random Variables and Stable Distributions on Fractal Cantor Sets
Fractal and Fractional, 2019 In this paper, we introduce the concept of fractal random variables and their related distribution functions and statistical properties. Fractal calculus is a generalisation of standard calculus which includes function with fractal support.
Alireza Khalili Golmankhaneh +1 more
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Reinforcement problems for variational inequalities on fractal sets [PDF]
, 2015 The aim of this paper is to study reinforcement problems for variational inequalities of the obstacle type on fractal ...
Capitanelli, Raffaela +1 more
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Generalized s-Convex Functions on Fractal Sets
Abstract and Applied Analysis, 2014 We introduce two kinds of generalized s-convex functions on real linear fractal sets Rα ...
Huixia Mo, Xin Sui
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