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

Purohit, Sunil D.; Suthar, Daya L.; Kalla, Shiam L.

Matematiche 67, No. 1, 21-32 (2012).

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, \({}_pF_q\)

Keywords:

Marichev-Saigo-Maeda fractional integral operators; Bessel function of first kind; generalized wright function; generalized hypergeometric series; cosine and sine functions

Software:

DLMF