Compositions of Saigo fractional integral operators with generalized Voigt function

Abstract

The principal object of this paper is to providethe composition of Saigo fractional integral operators withdifferent forms of Voigt functions. An alternative explicitrepresentation of the generalized Voigt function in terms ofLaplace integral transform is shown and the relations between theleft-sided and the right-sided Saigo fractional integral operatorsare established with the ${}_1{F}_1$-transform and the Whittakertransform, respectively. Many interesting results are deduced interms of some relatively more familiar hypergeometric functions inone and two variables.