The General Fractional Integrals and Derivatives on a Finite Interval
Mathematics, 2023 The general fractional integrals and derivatives considered so far in the Fractional Calculus literature have been defined for the functions on the real positive semi-axis.
Mohammed Al-Refai, Yuri Luchko
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General Fractional Integrals and Derivatives with the Sonine Kernels
Mathematics, 2021 In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero.
Yuri Luchko
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Numerical Approaches to Fractional Integrals and Derivatives: A Review
Mathematics, 2020 Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two main characteristics—singularity and nonlocality—has attracted increasing interest due to its potential applications in the real world.
Min Cai, Changpin Li
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Hermite-Hadamard, Trapezoid and Midpoint Type Inequalities Involving Generalized Fractional Integrals for Convex Functions [PDF]
Sahand Communications in Mathematical Analysis, 2023 We first construct new Hermite-Hadamard type inequalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard
Hasan Kara, Samet Erden, Huseyin Budak
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Fractional Integrals and Derivatives: “True” versus “False”
Mathematics, 2023 Within the last few years, many of the efforts of the fractional calculus (FC) community have been directed towards clarifying the nature and essential properties of the operators known as fractional integrals and derivatives [...]
Yuri Luchko
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Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial
Mathematics, 2019 Several fractional-order operators are available and an in-depth knowledge of the selected operator is necessary for the evaluation of fractional integrals and derivatives of even simple functions.
Roberto Garrappa +2 more
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Editorial for Special Issue “Fractional Calculus and Special Functions with Applications”
Fractal and Fractional, 2021 The study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications due to their properties of interpolation between operators of integer order [...]
Mehmet Ali Özarslan +2 more
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Desiderata for Fractional Derivatives and Integrals
Mathematics, 2019 The purpose of this brief article is to initiate discussions in this special issue by proposing desiderata for calling an operator a fractional derivative or a fractional integral.
Rudolf Hilfer, Yuri Luchko
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Fractional Calculus: Theory and Applications
Mathematics, 2018 Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons).[...]
Francesco Mainardi
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Katugampola Fractional Calculus With Generalized k−Wright Function
European Journal of Mathematical Analysis, 2021 In this article, we present some properties of the Katugampola fractional integrals and derivatives. Also, we study the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized k−Wright function nΦkm(z).
Ahmad Y. A. Salamooni, D. D. Pawar
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