Fractional integral operator associated with extended Mittag-Leffler function

Discrete Dynamics in Nature and Society

Manzoor

Amsalu

et al. 2021

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

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

Discrete Dynamics in Nature and Society

Manzoor

Amsalu

et al. 2021

Self Cite

“…exists whenever Rðln ½1 + ðδ − 1Þs/ðδ − 1ÞÞ > r, s ∈ C. The power function of the transform by Kumar [27] and Nadir and Khan [28] is given below:…”

Section: Introductionmentioning

confidence: 99%

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

Amsalu

Advances in Mathematical Physics

et al. 2021

Self Cite

In this paper, our leading objective is to relate the fractional integral operator known as P δ -transform with the ք -extended Mathieu series. We show that the P δ -transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the P δ -transform into a classical Laplace transform by changing the variable ln δ − 1 s + 1 / δ − 1 ⟶ s ; then, we get the integral involving the Laplace transform.

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

Manzoor

Advances in Mathematical Physics

Wubneh

et al. 2021

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.