Computation of certain integral formulas involving generalized Wright function

Abstract

The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions connected with the generalized Wright function are explicitly established as special cases for different values of the parameters. Moreover, a Gaussian quadrature formula has been used to compute the integrals and compare with the main results by using graphical representations.

Application of the Pathway-Type Transform to a New Form of a Fractional Kinetic Equation Involving the Generalized Incomplete Wright Hypergeometric Functions

“…where ϑ 1 , ϑ 2 , and ϑ 3 are complex parameters such that (ϑ 1 ) > 0, (ϑ 2 ) > 0, and (ϑ 3 ) > 0. Recent developments and expansions of Wright's hypergeometric function can be found, for example, in [29,30].…”

Certain Matrix Riemann–Liouville Fractional Integrals Associated with Functions Involving Generalized Bessel Matrix Polynomials

“…Recently, evaluations of fractional integral transforms involving a number of special functions including hypergeometric and generalized functions, generalized Wright functions, ℵ-functions, Bessel functions, Struve functions, and the Mittag-Leffler function and its various generalizations have played important roles in solving various problems related to the above-mentioned diverse research areas. For more detail, the interested reader may refer to some recent works (such as [1,[3][4][5]17,[31][32][33][34][35] and the references cited therein).…”