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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 ...
H. J. Haubold, A. M. Mathai, R. K. Saxena   +2 more
doaj   +5 more sources

Note on generalized Mittag-Leffler function. [PDF]

Springerplus, 2016
The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.
Desai R, Salehbhai IA, Shukla AK.
europepmc   +4 more sources

Why the Mittag-Leffler Function Can Be Considered the Queen Function of the Fractional Calculus? [PDF]

Entropy, 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 ...
Francesco Mainardi
doaj   +2 more sources

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 of the
Dinesh Kumar, Jeta Ram, Junesang Choi
doaj   +1 more source

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
doaj   +1 more source

Existence and Stability Results on Hadamard Type Fractional Time-Delay Semilinear Differential Equations

Mathematics, 2020
A delayed perturbation of the Mittag-Leffler type matrix function with logarithm is proposed. This combines the classic Mittag–Leffler type matrix function with a logarithm and delayed Mittag–Leffler type matrix function. With the help of this introduced
Nazim Mahmudov, Areen Al-Khateeb
doaj   +1 more source

Novel Generalized Low-Pass Filter with Adjustable Parameters of Exponential-Type Forgetting and Its Application to ECG Signal

Sensors, 2022
In this paper, a novel form of the Gaussian filter, the Mittag–Leffler filter is presented. This new filter uses the Mittag–Leffler function in the probability-density function.
Ivo Petráš
doaj   +1 more source

On Multi-Index Mittag–Leffler Function of Several Variables and Fractional Differential Equations

Journal of Mathematics, 2021
In this paper, we have studied a unified multi-index Mittag–Leffler function of several variables. An integral operator involving this Mittag–Leffler function is defined, and then, certain properties of the operator are established.
B. B. Jaimini, Manju Sharma, D. L. Suthar, S. D. Purohit   +3 more
doaj   +1 more source

Partial sums of Mittag-Leffler function [PDF]

Journal of Mathematical Inequalities, 2018
Summary: In the present investigation, Mittag-Leffler function with their normalization are considered. In this paper we will study the ratio of a function of the form \[ \mathbb{E}_{\lambda,\mu}(z)= \Gamma(\mu) zE_{\lambda,\mu}(z) :=\sum^\infty_{n=0} {\Gamma(\mu)\over \Gamma(\lambda n+\mu} z^{n+1}\qquad(z,\lambda,\mu\in \mathbb{C};\;\text{Re}(\lambda)>
ORHAN, Halit, Bansal, Deepak
openaire   +3 more sources

Taylor Series for the Mittag–Leffler Functions and Their Multi-Index Analogues

Mathematics, 2022
It has been obtained that the n-th derivative of the 2-parametric Mittag–Leffler function is a 3-parametric Mittag–Leffler function, with exactness to a constant.
Jordanka Paneva-Konovska
doaj   +1 more source