Geodesic
Fractional Integration of the Product of Bessel Functions of the First Kind
Fractional calculus and applied analysis, Tome 13 (2010) no. 2, pp. 159-176

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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.
Keywords: Fractional Integrals, Bessel Function of the First Kind, Generalized Hypergeometric Series, Generalized Lauricella Series in Several Variables, Cosine and Sine Trigonometric Functions 
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Kilbas, Anatoly; Sebastian, Nicy. Fractional Integration of the Product of Bessel Functions of the First Kind. Fractional calculus and applied analysis, Tome 13 (2010) no. 2, pp. 159-176. http://geodesic.mathdoc.fr/item/FCAA_2010_13_2_a2/