Progress in Fractional Differentiation & Applications
Article Title
The Multiple Composed Erde ́lyi-Kober Fractional Integrals and Derivatives and Their Convolutions
Abstract
This article addresses the multiple composed Erde ́lyi-Kober fractional derivatives and integrals that are compositions of the suitable right- and left-sided Erde ́lyi-Kober derivatives and integrals. These operators are important, say, in the framework of the Euler-Lagrange equations in the fractional calculus of variations. We start with a discussion of their properties including inversion formulas, compositions, and mapping properties. Then, we introduce an integral transform of the Mellin convolution type related to the multiple composed Erde ́lyi-Kober integrals and derive some operational relations. Finally, a one parameter family of convolutions for the multiple composed Erde ́lyi-Kober integrals in the sense of Dimovski is constructed
Digital Object Identifier (DOI)
http://dx.doi.org/10.18576/pfda/060301
Recommended Citation
Al-Kandari, Maryam; A-M. Hanna, Latif; and Luchko, Yuri
(2020)
"The Multiple Composed Erde ́lyi-Kober Fractional Integrals and Derivatives and Their Convolutions,"
Progress in Fractional Differentiation & Applications: Vol. 6:
Iss.
3, Article 1.
DOI: http://dx.doi.org/10.18576/pfda/060301
Available at:
https://digitalcommons.aaru.edu.jo/pfda/vol6/iss3/1