CERTAIN EXTENDED SPECIAL FUNCTIONS AND FRACTIONAL INTEGRAL AND DERIVATIVE OPERATORS VIA AN EXTENDED BETA FUNCTION

Abstract

Various extensions of the Euler’s beta function have, recently, been presented and investigated. Here, choosing to use a fully extended beta function, we introduce an extended hypergeometric function, an extended confluent hypergeometric function, and an extension of the Appell function F_1. We, also, use the fully extended beta function to introduce an extended Riemann-Liouville type integral operator and investigate its associated formulas and generating relations. The results presented here, being very general, can be specialized to yield some known and new results.