Certain properties of generalized \(M\)-series under generalized fractional integral operators (Q2240185)

Summary: The aim of this study is to introduce new (presumed) generalized fractional integral operators involving \(I\)-function as a kernel. In addition, two theorems have been developed under these operators that provide an image formula for this generalized \(M\)-series and also to study the different properties of the generalized \(M\)-series. The corresponding assertions in terms of Euler and Laplace transform methods are presented. Due to the general nature of the \(I\)-function and the generalized \(M\)-series, a number of results involving special functions can be achieved only by making appropriate values for the parameters.