October 2019 The decompositional structure of certain fractional integral operators
Min-Jie LUO, Ravinder Krishna RAINA
Hokkaido Math. J. 48(3): 611-650 (October 2019). DOI: 10.14492/hokmj/1573722020


The aim of this paper is to investigate the decompositional structure of generalized fractional integral operators whose kernels are the generalized hypergeometric functions of certain type. By using the Mellin transform theory proposed by Butzer and Jansche [J. Fourier Anal. 3 (1997), 325-376], we prove that these operators can be decomposed in terms of Laplace and inverse Laplace transforms. As applications, we derive two very general results involving the $H$-function. We also show that these fractional integral operators when being understood as integral equations possess the $\mathcal{L}$ and $\mathcal{L}^{-1}$ solutions. We also consider the applications of the decompositional structures of the fractional integral operators to some specific integral equations and one of such integral equations is shown to possess a solution in terms of an Aleph $(\aleph)$-function.


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Min-Jie LUO. Ravinder Krishna RAINA. "The decompositional structure of certain fractional integral operators." Hokkaido Math. J. 48 (3) 611 - 650, October 2019. https://doi.org/10.14492/hokmj/1573722020


Published: October 2019
First available in Project Euclid: 14 November 2019

zbMATH: 07145332
MathSciNet: MR4031254
Digital Object Identifier: 10.14492/hokmj/1573722020

Primary: 26A33 , 33C60 , 44A10 , 44A15 , 45E10

Keywords: $H$-function , fractional integral operator , generalized hypergeometric function , integral equation , Laplace transform , Mellin transform

Rights: Copyright © 2019 Hokkaido University, Department of Mathematics


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Vol.48 • No. 3 • October 2019
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