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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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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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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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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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The Minkowski inequalities via generalized proportional fractional integral operators
Advances in Difference Equations, 2019 Recent research has gained more attention on conformable integrals and derivatives to derive the various type of inequalities. One of the recent advancements in the field of fractional calculus is the generalized nonlocal proportional fractional ...
Gauhar Rahman +3 more
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Advances in Difference Equations, 2021 We investigate the existence of solutions for a system of Riemann–Liouville fractional differential equations with nonlinearities dependent on fractional integrals, subject to coupled nonlocal boundary conditions which contain various fractional ...
Rodica Luca
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