Generalized Fractional Integral Operators and M-Series

Abstract EN

Two fractional integral operators associated with Fox H-function due to Saxena and Kumbhat are applied to M-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric function pFq.

The Mellin and Whittaker transforms are obtained for these compositional operators with M-series.

Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators.

The results are expressed in terms of H-function, which are in compact form suitable for numerical computation.

Special cases of the results are also pointed out in the form of lemmas and corollaries.