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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, \({}_pF_q\)

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