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

Dinesh Kumar, D. Kumar

Abstract


Two integral transforms involving the function F3 occurring in the Kernels are considered. The function F3 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).


Keywords


Fractional Integrals, Bessel Functions of the First Kind, Generalized Hypergeometric Series, Generalized Lauricella Series in Several Variables, Appell Function- F3 , Cosine and Sine Trigonometric Functions

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