Fractional calculus and integral transforms of incomplete $\tau$-Hypergeometric Function

Neelam Pandey; Jai Prakash Patel

doi:10.4134/CKMS.c170036

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2018; 33(1): 127-142

Online first article June 9, 2017 Printed January 31, 2018

https://doi.org/10.4134/CKMS.c170036

Fractional calculus and integral transforms of incomplete $\tau$-Hypergeometric Function

Neelam Pandey, Jai Prakash Patel

A. P. S. University, A. P. S. University

Abstract

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Abstract

In the present article, authors obtained certain fractional derivative and integral formulas involving incomplete $\tau$-hypergeometric function introduced by Parmar and Saxena \cite{RKParmaRKSaxena1:2016}. Some interesting special cases and consequences of our main results are also considered.

Keywords: incomplete Pochhammer symbols, incomplete gamma function, generalized incomplete $\tau$-hypergeometric function, fractional derivative and integral operators

MSC numbers: Primary 26A33, 33B15, 33C05, 33C20, 44A10, 44A20; Secondary 33B99, 33C99, 33D90