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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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Fractional Integrals and Derivatives: Mapping Properties [PDF]
Fractional Calculus and Applied Analysis, 2016 This is a fundamental survey of numerous results devoted to mapping properties of diverse modifications of fractional integrals (in one and many dimensions) in a variety of function spaces. The main focus is on fractional integrals of variable order and function spaces with variable exponents.
Rafeiro Humberto +2 more
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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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General Fractional Integrals and Derivatives of Arbitrary Order [PDF]
Symmetry, 2021 In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced.
Yuri Luchko, Luchko Yuri
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Calculus of variations with fractional derivatives and fractional integrals [PDF]
Applied Mathematics Letters, 2009 We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Ricardo Almeida, Delfim F M Torres
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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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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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Evaluation of Fractional Integrals and Derivatives of Elementary Functions: Overview and Tutorial [PDF]
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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A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives [PDF]
Chaos, Solitons and Fractals, 2017 This is a preprint of a paper whose final and definite form is with 'Chaos, Solitons & Fractals', ISSN: 0960-0779. Submitted 1 Dec 2016; Article revised 17 Apr 2017; Article accepted for publication 19 Apr 2017; see [http://dx.doi.org/10.1016/j.chaos.2017.04.034]
E Babolian, Delfim F M Torres
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Approximation of fractional integrals by means of derivatives
Computers and Mathematics With Applications, 2012 We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to develop suitable numerical approximations with known estimations for the error.
Shakoor Pooseh +2 more
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