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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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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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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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Non-local Integrals and Derivatives on Fractal Sets with Applications
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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Generalized escape criteria for fractals via convex viscosity approximation iterations. [PDF]
PLoS ONEIn this manuscript, we present the generation of Mandelbrot sets, Julia set fractals, and Biomorphs using a two-step viscosity approximation method applied to the complex function [Formula: see text], where [Formula: see text] and [Formula: see text ...
Shuai Wang +4 more
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Mathematics, 2023 In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite–Hadamard-type inequality using generalized (E,h)-convexity and obtain two
Wedad Saleh +3 more
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Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution.
Pierre Arnoux +3 more
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Analysis of fractal-fractional model of tumor-immune interaction
Results in Physics, 2021 Recently, Atangana proposed new operators by combining the fractional and fractal calculus. These recently proposed operators, referred to as fractal-fractional operators, have been widely used to study the complex dynamics of a problem.
Shabir Ahmad +4 more
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From Fractal Geometry to Statistical Fractal
Recoletos Multidisciplinary Research Journal, 2013 The development from fractal geometry to fractal statistics was established in this paper. Interesting features such as self similarity, scale invariance, and the spacefilling property of objects (fractal dimension) of fractal geometry provided an ...
Roberto N. Padua, Mark S. Borres
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Fractal Curves on Banach Algebras
Fractal and Fractional, 2022 Most of the fractal functions studied so far run through numerical values. Usually they are supported on sets of real numbers or in a complex field. This paper is devoted to the construction of fractal curves with values in abstract settings such as ...
María A. Navascués
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