Beta Operator with Caputo Marichev-Saigo-Maeda Fractional Differential Operator of Extended Mittag-Leffler Function

Abstract

In this paper, a beta operator is used with Caputo Marichev-Saigo-Maeda (MSM) fractional differentiation of extended Mittag-Leffler function in terms of beta function. Further in this paper, some corollaries and consequences are shown that are the special cases of our main findings. We apply the beta operator on the right-sided MSM fractional differential operator and on the left-sided MSM fractional differential operator. We also apply beta operator on the right-sided MSM fractional differential operator with Mittag-Leffler function and the left-sided MSM fractional differential operator with Mittag-Leffler function.

Two Dimensional Laplace Transform Coupled with the Marichev-Saigo-Maeda Integral Operator and the Generalized Incomplete Hypergeometric Function

“…In terms of the Laplace function, Khan et al [1] constructed a Laplace operator using the Caputo fractional differentiation of the extended Mittag-Leffler function. Manzoor et al [2] developed a Beta operator in terms that was based on the extended Mittag-Leffler function with Caputo fractional differentiation. Bansal et al [3] used the well-known integral transform to solve the fractional kinetic equation (FKE) associated with the incomplete I-function (IIF) (Laplace transform).…”

Fractional Operators Associated with the ք -Extended Mathieu Series by Using Laplace Transform

“…Manzoor et al [5] used a Beta operator with Caputo (MSM) fractional differentiation of extended Mittag-Leffler function in terms of Beta function. They applied the Beta operator on the right-sided MSM fractional differential operator and on the left-sided MSM fractional differential operator.…”