Fractional calculus operator with generalize k-Mittag-Leffler function

Abstract

In this paper, we introduce and investigate a fractional calculus with an integral operator which contains the family of generalized k-Mittag-Leffler function in its kernel, (λ)_ν being the familiar pochhammer symbol. We also find solution of differential equation of fractional order based upon the Hilfer derivatives operator and containing this integral operator by using Sumudu transform technique.

Subject Classification:

• 26 A33
• 33E12
• 34A08

Keywords:

• Generalized k-Mittag-Leffler functions
• Hilfer fractional operator
• Sumudu transform
• fractional differential equations
• Fox-write pΨq -function
• k-gamma functions