Results 11 to 20 of about 1,811 (235)
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
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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 [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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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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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 engineering.
Oliveira, Edmundo Capelas de +1 more
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Theory of Functional Connections Extended to Fractional Operators
Mathematics, 2023 The theory of functional connections, an analytical framework generalizing interpolation, was extended and applied in the context of fractional-order operators (integrals and derivatives).
Daniele Mortari +2 more
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Research on Two Types of Fractional Integrals
, 2022 : In this paper, based on Jumarie type of Riemann-Liouville (R-L) fractional calculus, we solve two types of fractional integrals. Complex power of fractional analytic function, product rule for fractional derivatives and a new multiplication of ...
Chii-Huei Yu
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On a Fractional Differential Equation with r-Laplacian Operator and Nonlocal Boundary Conditions
Mathematics, 2022 We study the existence and multiplicity of positive solutions of a Riemann-Liouville fractional differential equation with r-Laplacian operator and a singular nonnegative nonlinearity dependent on fractional integrals, subject to nonlocal boundary ...
Johnny Henderson +2 more
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Fractional variational problems depending on indefinite integrals [PDF]
, 2012 We obtain necessary optimality conditions for variational problems with a Lagrangian depending on a Caputo fractional derivative, a fractional and an indefinite integral.
Pooseh, Shakoor +8 more
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Fractional variational problems with the Riesz-Caputo derivative [PDF]
, 2012 In this paper we investigate optimality conditions for fractional variational problems, with a Lagrangian depending on the Riesz-Caputo derivative. First we prove a generalized Euler-Lagrange equation for the case when the interval of integration of the ...
Almeida, R. +2 more
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