Fractional Integrals Bessel Function of the First Kind Generalized Hypergeometric Series Generalized Lauricella Series in Several Variables Cosine and Sine Trigonometric Functions
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Fractional Calculus and Applied Analysis, Vol. 13, No 2, (2010), 159p-176p
Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober 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 Lau-ricella function due to Srivastava and Daoust. Corresponding assertions for the Riemann-Liouville and Erdélyi-Kober fractional integrals are presented.
Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50,