Results 1 to 10 of about 9,626 (263)
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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Optimization on fractal sets [PDF]
Optimization Letters, 2021 We outline necessary and sufficient condition to the existence of extrmas of a function on a self-similar set, and we describe discrete gradient algorithm to find the extrema.
Nizare Riane, Claire David
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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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Turbulence on a Fractal Fourier Set [PDF]
Physical Review Letters, 2015 A novel investigation of the nature of intermittency in incompressible, homogeneous and isotropic turbulence is performed by a numerical study of the Navier-Stokes equations constrained on a fractal Fourier set. The robustness of the energy transfer and of the vortex stretching mechanisms is tested by changing the fractal dimension, D, from the ...
Lanotte, As +4 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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From Fractal Groups to Fractal Sets [PDF]
, 2003 This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and renormalizable dynamical systems.
Bartholdi, Laurent +2 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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