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.

Certain fractional calculus formulas involving extended generalized Mathieu series

“…For various investigations involving the Hadamard product (or the convolution), the interested reader may refer to recent papers on the subject (see, for example, [68,69] and the references cited therein). Also we require the Fox-Wright function p q (z) (p, q ∈ N 0 ) with p numerator and q denominator parameters defined for a 1 , .…”

A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel–Wright Function

“…Recently, Agarwal et al [25] found the solution of non-homogeneous time fractional heat equation and fractional Volterra integral equation using integral transform of pathway type. Also, Srivastava et al [26] and [27] found some results involving generalized hypergeometric function and generalized incomplete gamma function by using P δ -transform.…”

Fractional Integration and Differentiation of the Generalized Mathieu Series

“…For various other investigations involving the Hadamard product (or the convolution), the interested reader may be referred to several recent papers on the subject (see, for example, [27,28] and the references cited in each of these papers).…”