Fractional integrals and derivatives: mapping properties [PDF]
Fractional Calculus and Applied Analysis, 2016 This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known,
Rafeiro, Humberto, Samko, Stefan
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Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics [PDF]
Abstract and Applied Analysis, 2012 We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives.
Tatiana Odzijewicz +2 more
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An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order [PDF]
The Scientific World Journal, 2013 We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given.
Ricardo Almeida, Delfim F. M. Torres
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Desiderata for Fractional Derivatives and Integrals [PDF]
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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A Review of Definitions for Fractional Derivatives and Integral [PDF]
Mathematical Problems in Engineering, 2014 This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and ...
Machado, J. A. Tenreiro +1 more
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Fractional integrals, derivatives and integral equations with weighted Takagi–Landsberg functions
Nonlinear Analysis: Modelling and Control, 2020 In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under Schauder basis.
Vitalii Makogin, Yuliya Mishura
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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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Generalized fractional Hilfer integral and derivative
Contributions to Mathematics, 2020 Juan E. Nápoles Valdés
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On generalized fractal-fractional derivative and integral operators associated with generalized Mittag-Leffler function. [PDF]
HeliyonKhan H +4 more
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Nabla Fractional Derivative and Fractional Integral on Time Scales [PDF]
Axioms, 2021 In this paper, we introduce the nabla fractional derivative and fractional integral on time scales in the Riemann–Liouville sense. We also introduce the nabla fractional derivative in Grünwald–Letnikov sense. Some of the basic properties and theorems related to nabla fractional calculus are discussed.
Bikash Gogoi +4 more
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