Generalized Fractional Integral Operators andM-Series

Abstract

Two fractional integral operators associated with FoxH-function due to Saxena and Kumbhat are applied toM-series, which is an extension of both Mittag-Leffler function and generalized hypergeometric functionpFq. The Mellin and Whittaker transforms are obtained for these compositional operators withM-series. Further some interesting properties have been established including power function and Riemann-Liouville fractional integral operators. The results are expressed in terms ofH-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.

Certain Properties of Generalized M-Series under Generalized Fractional Integral Operators

“…In this study, we introduced and studied the properties of generalized M-series under the new (presumed) generalized fractional integral operators which are defined in equations ( 6) and ( 7) and also developed some new images. e results established in this study contain various special cases, such that if we take r � 1, we recover the known results recorded in [20]. Furthermore, we can present certain very interesting results in the form of several theorems associated with Mellin, Whittaker, and K-transforms.…”