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Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications

School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
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Mathematics 2019, 7(6), 517; https://doi.org/10.3390/math7060517
Received: 28 April 2019 / Revised: 30 May 2019 / Accepted: 5 June 2019 / Published: 6 June 2019
(This article belongs to the Special Issue Applied Functional Analysis and Its Applications)
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Abstract

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 integral equations, fractional differential equations, and fractional integrodifferential equations. Our main goal is to present some new properties for ψ-fractional integrals involving a general function ψ by establishing several new equalities for the ψ-fractional integrals. We also give two applications of our new equalities. View Full-Text
Keywords: fractional calculus; ψ-fractional integrals; fractional differential equations fractional calculus; ψ-fractional integrals; fractional differential equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Liang, J.; Mu, Y. Properties for ψ-Fractional Integrals Involving a General Function ψ and Applications. Mathematics 2019, 7, 517.

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