Fractional Integration of Generalized Bessel Function of the First Kind

Generalizing the classical Riemann-Liouville and Erde´yi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.