2020•Journal | MESARequires access

New composition formulae for the generalized fractional calculus operators with the extended Mittag-Leffler function

D. L. Suthar, Biniyam Shimelis, Nigussie Abeye, Hafte Amsalu

Abstract

The aim of this paper is to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators involving Appell function applied on the extended generalized Mittag-Leffler function (EGMLF). The results are expressed in terms of extended Wright function. As special cases, the corresponding assertions for Saigo and Erd$\acute{e}$lyi -Kober fractional operators are presented and also the effect of MSM fractional calculus operators on the another type of generalized Mittag-Leffler functions, extended confluent hypergeometric functions and extended Mittag-Leffler functions are studied.

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Key concepts: Fractional calculus, Mathematics, Special functions, Mittag-Leffler function, Hypergeometric function, Generalized function, Function (biology), Operational calculus