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 +2 more
doaj +5 more sources
Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function [PDF]
Mathematics, 2020 We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [Fract. Calc. Appl. Anal. 21 (2018) 1156−1169].
Richard Paris
doaj +2 more sources
On Modifications of the Gamma Function by Using Mittag-Leffler Function [PDF]
Journal of Mathematics, 2021 Mittag-Leffler function is a natural generalization of the exponential function. Recent applications of Mittag-Leffler function have reshaped the scientific literature due to its fractional effects that cannot be obtained by using exponential function ...
Asifa Tassaddiq, Abdulrahman Alruban
doaj +2 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
Close-to-convexity and partial sums for normalized Le Roy-type $ q $-Mittag-Leffler functions
AIMS MathematicsIn recent years, researchers have explored the properties of close-to-convexity and partial sums for various Mittag-Leffler functions, including $ q $-Mittag-Leffler, Bernas Mittag-Leffler, and Le Roy-type Mittag-Leffler functions.
Khaled Matarneh +4 more
doaj +2 more sources
The Mittag-Leffler Fitting of the Phillips Curve
Mathematics, 2019 In this paper, a mathematical model based on the one-parameter Mittag-Leffler function is proposed to be used for the first time to describe the relation between the unemployment rate and the inflation rate, also known as the Phillips curve. The Phillips
Tomas Skovranek
doaj +3 more sources
Parsimonious Continuous Time Random Walk Models and Kurtosis for Diffusion in Magnetic Resonance of Biological Tissue [PDF]
Frontiers in Physics, 2015 In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue.
Carson eIngo +5 more
doaj +3 more sources
Self-similar Cauchy problems and generalized Mittag-Leffler functions [PDF]
, 2019 By observing that the fractional Caputo derivative can be expressed in terms of a multiplicative convolution operator, we introduce and study a class of such operators which also have the same self-similarity property as the Caputo derivative. We proceed
Pierre Patie, Anna Srapionyan
openalex +3 more sources
On generalized fractal-fractional derivative and integral operators associated with generalized Mittag-Leffler function. [PDF]
HeliyonKhan H +4 more
europepmc +2 more sources
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)>
Deepak Bansal, Halit Orhan
openalex +4 more sources