Results 21 to 30 of about 1,105 (254)
Fractal and Fractional, 2023 In this study, we delve into the general theory of operator kernel functions (OKFs) in operational calculus (OC). We established the rigorous mapping relation between the kernel function and the corresponding operator through the primary translation ...
Xiaobin Yu, Yajun Yin
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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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Fractional calculus and the evolution of fractal phenomena [PDF]
Physica A: Statistical Mechanics and its Applications, 1999 It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal
Rocco, A, West, BJ
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Fuzzification of Fractal Calculus
, 2023 In this manuscript, fractal and fuzzy calculus are summarized. Fuzzy calculus in terms of fractal limit, continuity, its derivative, and integral are formulated. The fractal fuzzy calculus is a new framework that includes fractal fuzzy derivatives and fractal fuzzy integral.
Golmankhaneh, Alireza Khalili +3 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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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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Fractal-fractional Anthroponotic Cutaneous Leishmania model study in sense of Caputo derivative
Alexandria Engineering Journal, 2022 The current paper is the analysis of an Anthroponotic Cutaneous Leishmania infection caused by a parasite known as Leishmania Tropica under the Caputo fractal-fractional operator.
Lei Zhang +4 more
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Sobolev Spaces and Calculus of Variations on Fractals [PDF]
, 2020 The present note contains a review of $p$-energies and Sobolev spaces on metric measure spaces that carry a strongly local regular Dirichlet form. These Sobolev spaces are then used to generalize some basic results from the calculus of variations, such as the existence of minimizers for convex functionals and certain constrained mimimization problems ...
Hinz, Michael +2 more
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Alexandria Engineering Journal, 2020 Local fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time.
Kang-Jia Wang, Hong-Chang Sun, Zhe Fei
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Special Issue: Fractal Functions and Applications
Fractal and Fractional, 2022 This volume gathers some important advances in the fields of fractional calculus and fractal curves and functions [...]
María Antonia Navascués +1 more
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