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A Two-Way Convolution of the Mittag-Leffler Function with Sheffer Polynomials

Mathematics
This article presents a two-way convolution of the Mittag-Leffler function with Sheffer polynomials via the umbral algebraic method, thereby introducing the Mittag-Leffler–Sheffer polynomials (MLSPs) and the Sheffer–Mittag-Leffler function (SMLF).
Waseem Ahmad Khan, Areefa Khatoon, Khidir Shaib Mohamed, Muntasir Suhail, Habeeb Ibrahim, Naglaa Mohammed   +5 more
doaj   +2 more sources

Mittag-Leffler Functions and Their Applications [PDF]

Journal of Applied Mathematics, 2011
Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief survey of the Mittag-Leffler function ...
H. J. Haubold, A. M. Mathai, R. K. Saxena   +2 more
doaj   +2 more sources

Some Remarks on Estimate of Mittag-Leffler Function

Journal of Function Spaces, 2019
The estimate of Mittag-Leffler function has been widely applied in the dynamic analysis of fractional-order systems in some recently published papers. In this paper, we show that the estimate for Mittag-Leffler function is not correct.
Jia Jia, Zhen Wang, Xia Huang, Yunliang Wei   +3 more
doaj   +2 more sources

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

Discrete Dynamics in Nature and Society, 2021
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.
Adnan Khan, Tayyaba Manzoor, Hafte Amsalu Kahsay, Kahsay Godifey Wubneh   +3 more
doaj   +2 more sources

Differential Subordination and Superordination Results Associated with Mittag–Leffler Function

Mathematics, 2021
In this paper, we derive a number of interesting results concerning subordination and superordination relations for certain analytic functions associated with an extension of the Mittag–Leffler function.
A. Attiya, M. Aouf, E. E. Ali, M. F. Yassen   +3 more
semanticscholar   +2 more sources

Fractional derivatives of the generalized Mittag-Leffler functions

Advances in Difference Equations, 2018
In this paper, we derive the compositions of the fractional derivatives with the Shukla function, a four-parameter Mittag-Leffler function. We investigate and compare the difference between the Riemann–Liouville and Caputo derivatives of the generalized ...
Denghao Pang, Wei Jiang, Azmat U. K. Niazi   +2 more
doaj   +2 more sources

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

Advances in Mathematical Physics, 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.
Tayyaba Manzoor, Adnan Khan, Kahsay Godifey Wubneh, Hafte Amsalu Kahsay   +3 more
doaj   +2 more sources

On the solutions of certain fractional kinetic equations involving k-Mittag-Leffler function

Advances in Differential Equations, 2018
The aim of the present paper is to develop a new generalized form of the fractional kinetic equation involving a generalized k-Mittag-Leffler function Ek,ζ,ηγ,ρ(⋅)$E^{\gamma,\rho}_{k,\zeta,\eta}(\cdot)$.
Praveen Agarwal, M. Chand, D. Băleanu, D. O'Regan, Shilpi Jain   +4 more
semanticscholar   +2 more sources

Turán type inequalities for generalized Mittag-Leffler function. [PDF]

J Inequal Appl, 2017
In this paper, we show several Turán type inequalities for a generalized Mittag-Leffler function with four parameters via the ( p , k ) $(p,k)$ -gamma ...
Dou XK, Yin L.
europepmc   +2 more sources

Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function. [PDF]

J Inequal Appl, 2017
The objective of this paper is to establish some new refinements of fractional Hermite-Hadamard inequalities via a harmonically convex function with a kernel containing the generalized Mittag-Leffler ...
Mihai MV, Awan MU, Noor MA, Noor KI.
europepmc   +2 more sources