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Complexity and the Fractional Calculus [PDF]
Advances in Mathematical Physics, 2013 We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler ...
Pramukkul, Pensri +4 more
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A Stochastic Fractional Calculus with Applications to Variational Principles
Fractal and Fractional, 2020 We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes.
Houssine Zine, Delfim F. M. Torres
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On the solutions of some fractional q-differential equations with the Riemann-Liouville fractional q-derivative [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 This paper is devoted to explicit and numerical solutions to linear fractional q-difference equations and the Cauchy type problem associated with the Riemann-Liouville fractional q-derivative in q-calculus.
S. Shaimardan, N.S. Tokmagambetov
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General Fractional Calculus: Multi-Kernel Approach [PDF]
Mathematics, 2021 For the first time, a general fractional calculus of arbitrary order was proposed by Yuri Luchko in 2021. In Luchko works, the proposed approaches to formulate this calculus are based either on the power of one Sonin kernel or the convolution of one ...
V. Tarasov
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Enhancing the Mathematical Theory of Nabla Tempered Fractional Calculus: Several Useful Equations
Fractal and Fractional, 2023 Although many applications of fractional calculus have been reported in literature, modeling the physical world using this technique is still a challenge. One of the main difficulties in solving this problem is that the long memory property is necessary,
Yiheng Wei +3 more
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Advances in Differential Equations, 2021 Fractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds.
A. Atangana
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A practical guide to Prabhakar fractional calculus [PDF]
Fractional Calculus and Applied Analysis, 2020 The Mittag–Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from the three-parameter generalization of this function, known as the ...
A. Giusti +6 more
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On tempered fractional calculus with respect to functions and the associated fractional differential equations [PDF]
Mathematical methods in the applied sciences, 2021 The prime aim of the present paper is to continue developing the theory of tempered fractional integrals and derivatives of a function with respect to another function.
Ashwini D. Mali +3 more
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On fractional Hahn calculus [PDF]
Advances in Difference Equations, 2017 Abstract In this paper, the new concepts of Hahn difference operators are introduced. The properties of fractional Hahn calculus in the sense of a forward Hahn difference operator are introduced and developed.
Thanin Sitthiwirattham +1 more
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