## Marichev-Saigo-Maeda fractional integration operators of the Bessel functions.(English)Zbl 1247.26012

Summary: We apply generalized operators of fractional integration involving Appell’s function $$F_3$$(.) due to Marichev-Saigo-Maeda, to the Bessel function of first kind. The results are expressed in terms of generalized Wright function and hypergeometric functions $$_pF_q$$. Special cases involving this function are mentioned. Results given recently by Kilbas and Sebastian follow as special cases of the theorems establish here.

### MSC:

 26A33 Fractional derivatives and integrals 33C05 Classical hypergeometric functions, $${}_2F_1$$ 33C10 Bessel and Airy functions, cylinder functions, $${}_0F_1$$ 33C20 Generalized hypergeometric series, $${}_pF_q$$

DLMF
Full Text: