Abstract
Several fractional calculus operators have been introduced and investigated. In this sequence, we aim to establish the Marichev-Saigo-Maeda (MSM) fractional calculus operators and Caputo-type MSM fractional differential operators of extended Mittag-Leffler function (EMLF). We also investigate the statistical distribution associated with the EMLF. Finally, we derive some of the particular cases of the main results.
Highlights
Introduction and PreliminariesFractional calculus (FC) is a discipline of mathematics that derives from the conventional definitions of integral and derivative operators by considering fractional values
The fractal calculus can efficiently deal with kinetics, which is termed the fractal kinetics [1,2,3]
The objective of this paper is to present generalized fractional integral and differential operators of extended Mittag-Leffler function (EMLF) and their application to statistical distribution
Summary
Fractional calculus (FC) is a discipline of mathematics that derives from the conventional definitions of integral and derivative operators by considering fractional values. 53, Equation (6)) as a kernel (see [28,29]): The generalized fractional integral operators involving the Appell functions F3 are defined for ν, ν0 , ξ, ξ 0 , θ ∈ C with 0 and x ∈ R+ as follows: ν,ν0 ,ξ,ξ 0 ,θ. Many researchers (see [30,31,32,33,34,35,36]) have studied the image formulas for MSM fractional integral operators involving various special functions. The objective of this paper is to present generalized fractional integral and differential operators of EMLF and their application to statistical distribution. The presented work is arranged as follows: In. Sections 2 and 3, a form of MSM fractional integral and differential representations of (5) is presented alongside its properties.
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