Laplace Operator with Caputo-Type Marichev–Saigo–Maeda Fractional Differential Operator of Extended Mittag-Leffler Function

Abstract

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

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

“…The solutions are represented in terms of the incomplete I-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.…”