On a general theorem connecting Laplace transform and generalized Weyl fractional integral operator

Abstract

The main aim of the present paper is to establish a general theorem which asserts an interesting relationship between the Laplace transform and generalized Weyl fractional integral operator involving general class of functions. Our main theorem involves a multidimensional series with essentially arbitrary sequence of complex numbers. By suitably assigning different values to the sequence, one can easily evaluate generalized Weyl fractional integral operator of special functions of several variables. An illustration for generalized Lauricella function is mentioned. Several interesting special cases of the general theorem are also mentioned.