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The Multiple Composed Erde ́lyi-Kober Fractional Integrals and Derivatives and Their Convolutions |
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PP: 153-167 |
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doi:10.18576/pfda/060301
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Author(s) |
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Maryam Al-Kandari,
Latif A-M. Hanna,
Yuri Luchko,
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Abstract |
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| 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 |
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