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Weighted Fractional Calculus: A General Class of Operators
Fractal and Fractional, 2022 We conduct a formal study of a particular class of fractional operators, namely weighted fractional calculus, and its extension to the more general class known as weighted fractional calculus with respect to functions.
Hafiz Muhammad Fahad, Arran Fernandez
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General Fractional Vector Calculus
Mathematics, 2021 A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators.
Vasily E. Tarasov
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A Stochastic Fractional Calculus with Applications to Variational Principles [PDF]
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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General Fractional Calculus: Multi-Kernel Approach
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 ...
Vasily E. Tarasov
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General Fractional Calculus in Multi-Dimensional Space: Riesz Form
Mathematics, 2023 An extension of the general fractional calculus (GFC) is proposed as a generalization of the Riesz fractional calculus, which was suggested by Marsel Riesz in 1949.
Vasily E. Tarasov
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Fuzzy clustering to classify several regression models with fractional Brownian motion errors
Alexandria Engineering Journal, 2020 Clustering regression models fitted on the dataset is one of the most ubiquitous issues in different fields of sciences. In this research, fuzzy clustering method is used to cluster regression models with fractional Brownian motion errors that can be ...
Mohammad Reza Mahmoudi +2 more
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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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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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Fractal and Fractional, 2022 In this study, the variable order fractional calculus of the hidden variable fractal interpolation function is explored. It extends the constant order fractional calculus to the case of variable order. The Riemann–Liouville and the Weyl–Marchaud variable
Valarmathi Raja, Arulprakash Gowrisankar
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Some trapezoid and midpoint type inequalities via fractional ( p , q ) $(p,q)$ -calculus
Advances in Difference Equations, 2021 Fractional calculus is the field of mathematical analysis that investigates and applies integrals and derivatives of arbitrary order. Fractional q-calculus has been investigated and applied in a variety of research subjects including the fractional q ...
Pheak Neang +4 more
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