Fractional integrals and solution of fractional kinetic equations involvingk-Mittag-Leffler function

Abstract

In this paper, our main objective is to establish certain new fractional integral by applying the Saigo hypergeometric fractional integral operators and by employing some integral transforms on the resulting formulas, we presented their image formulas involving the product of the generalized k-Mittag-Leffler function. Furthermore, We develop a new and further generalized form of the fractional kinetic equation involving the product of the generalized k-Mittag-Leffler function. The manifold generality of the generalized k-Mittag-Leffler function is discussed in terms of the solution of the fractional kinetic equation and their graphical interpretation is interpreted in the present paper. The results obtained here are quite general in nature and capable of yielding a very large number of known and (presumably) new results.

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