### The Product of Bessel Functions of the First Kind with Fractional Calculus Operators Involving Appell Hypergeometric Function

#### Abstract

Two integral transforms involving the function *F*_{3} occurring in the Kernels are considered. The function *F*_{3} is the familiar Appell Hypergeometric function. They generalize the Saigo and classical Riemann-Liouville fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine and sine functions are given. The results are established in terms of generalized Lauricella function due to Srivastava and Daoust. Corresponding assertions for the Saigo and Riemann-Liouville fractional integrals are presented. (AMS subject classification 33C10, 33C45, 26C33).

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