A Family of the Incomplete Hypergeometric Functions and Associated Integral Transform and Fractional Derivative Formulas

Abstract

Recently, Srivastava et al. [Integral Transforms Spec. Funct.
23 (2012), 659-683] introduced the
incomplete Pochhammer symbols that led to a natural generalization
and decomposition of a class of hypergeometric and other related functions
as well as to certain potentially useful closed-form representations
of definite and improper integrals of various special functions of applied mathematics
and mathematical physics. In the present paper, our aim is to establish
several formulas involving integral transforms and fractional derivatives of this
family of incomplete hypergeometric functions. As corollaries and consequences,
many interesting results are shown to follow from our main results.