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Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications
Mathematics, 2019 In this paper, we are concerned with the ψ-fractional integrals, which is a generalization of the well-known Riemann−Liouville fractional integrals and the Hadamard fractional integrals, and are useful in the study of various fractional ...
Jin Liang, Yunyi Mu
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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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New generalized Pólya–Szegö and Čebyšev type inequalities with general kernel and measure
Advances in Difference Equations, 2020 It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class C ( h ) $\mathfrak{C(h)}$ of functions which can be represented in a form of integral transforms involving general kernel ...
S. Iqbal +5 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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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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Fractional boundary value problems: Analysis and numerical methods [PDF]
, 2011 This is the author's PDF of an article published in Fractional Calculus and Applied Analysis 2011. The original publication is available at www.springerlink.comThis journal article discusses nonlinear boundary value problems.Fundacao para a Ciencia e ...
M. Luísa Morgado +3 more
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Advances in Difference Equations, 2020 The primary objective of this present paper is to establish certain new weighted fractional Pólya–Szegö and Chebyshev type integral inequalities by employing the generalized weighted fractional integral involving another function Ψ in the kernel.
Kottakkaran Sooppy Nisar +4 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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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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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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