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

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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