A Comparative Analysis of Modified Extended Fractional Derivative and Integral Operators Via Modified Extended Beta Function with Applications to Generating Functions

Year 2022, Volume: 19 Issue: 1, 40 - 50, 01.05.2022

Umar Muhammad Abubakar

Abstract

This article object is to introduce new extension of the extended beta, Gauss
hypergeometric, Appell hypergeometric and Lauricella hypergeometric functions. The
new extension of the extended Riemann-Liouville, Caputo and Kober-Erdelyi fractional
derivative and integral operators are also examined with their applications to generating
functions by considering the extended hypergeometric functions. The Mellin of certain
new extension of the extended fractional derivative and integral operators ware obtained.

Keywords

Beta function, Fractional calculus, Gamma function, Mellin transform.

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