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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, generalized Mittag‐Leffler functions, Mittag‐Leffler type functions, and their interesting and useful ...
Hans J. Haubold, Arak M. Mathai, Ram K. Saxena   +2 more
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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. First, we point out the mistakes made in the estimation process of Mittag-Leffler function and provide a ...
Jia Jia, Zhen Wang, Xia Huang, Yunliang Wei   +3 more
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Dirichlet Averages of Generalized Mittag-Leffler Type Function

Fractal and Fractional, 2022
Since Gösta Magus Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903 and studied its features in five subsequent notes, passing the first half of the 20th century during which the majority of scientists remained almost unaware ...
Jeta Ram, Junesang Choi, Dinesh Kumar
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On the p-k-Mittag-Leffler function [PDF]

Applied Mathematical Sciences, 2017
In this paper, we define the function pEk;;(z), estudy its analyticproperties, some elementary properties as its integral expression,its relationship with the fractional operator of Riemann-Liouville and investigatethe fractional generalization of the kinetic equation involvingthis Mittag-Leffler type function.
Cerutti, Ruben Alejandro, Luque, Luciano Leonardo, Dorrego, Gustavo   +2 more
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Generalized Integral Transform and Fractional Calculus Operators Involving a Generalized Mittag-Leffler (ML)-Type Function

Computer Sciences & Mathematics Forum, 2023
In this paper, we consider a generalized Mittag-Leffler (ML)-type function and establish several integral formulas involving Jacobi and related transforms. We also establish some of the composition of generalized fractional derivative formulas associated
Ankit Pal
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Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus? [PDF]

Entropy (Basel), 2020
In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from being the ...
Mainardi F.
europepmc   +3 more sources

Numerical evaluation of Mittag-Leffler functions

Calcolo, 2021
The Mittag-Leffler function is computed via a quadrature approximation of a contour integral representation. We compare results for parabolic and hyperbolic contours, and give special attention to evaluation on the real line. The main point of difference with respect to similar approaches from the literature is the way that poles in the integrand are ...
McLean, W ; https://orcid.org/
openaire   +6 more sources

On asymptotics of discrete Mittag-Leffler function [PDF]

Mathematica Bohemica, 2014
On the base of the backward fractional \(h\)-sum \[ \nabla_h^{-\mu} f(t_n) := \frac{h}{\Gamma_h(\mu)} \sum\limits_{k=1}^{n} (t_{n-k+1})_h^{(\mu-1)} f(t_k),\tag{1} \] the following fractional \(h\)-differences are considered -- the Riemann-Liouville backward fractional \(h\)-differences \[ {}_{\text{R-L}} \nabla_h^{\alpha} f(t_n) := \nabla_h \nabla_h^{-(
Nechvátal, Luděk
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Certain Unified Integrals Involving a Multivariate Mittag–Leffler Function

Axioms, 2021
A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with the same technique as Choi and Agarwal, we propose the establishment of two generalized integral formulas involving a multivariate ...
Praveen Agarwal, Prakash Singh, Shilpi Jain, Ravi P. Agarwal   +3 more
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A Matrix Mittag–Leffler Function and the Fractional Nonlinear Partial Integro-Differential Equation in ℝn

Fractal and Fractional, 2023
In this paper, we introduce the matrix Mittag–Leffler function, which is a generalization of the multivariate Mittag–Leffler function, in order to investigate the uniqueness of the solutions to a fractional nonlinear partial integro-differential equation
Joshua Beaudin, Azedine Rahmoune, Chenkuan Li, Walid Remili   +3 more
core   +2 more sources