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Comments on the properties of Mittag-Leffler function [PDF]
The European Physical Journal Special Topics, 2017 The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to define the relevant semigroup properties. We analyse the relevant role in the solution of Schrödinger type and heat-type fractional partial differential equations and explore ...
Dattoli G. +4 more
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Novel Low-Pass Two-Dimensional Mittag–Leffler Filter and Its Application in Image Processing
Fractal and Fractional, 2023 This paper presents an innovative Mittag–Leffler two-dimensional filter and its application in image processing. The proposed filter leverages the utilization of a Mittag–Leffler function within the probability density function.
Ivo Petráš
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Estimations of fractional integral operators for convex functions and related results
Advances in Difference Equations, 2020 This research investigates the bounds of fractional integral operators containing an extended generalized Mittag-Leffler function as a kernel via several kinds of convexity.
Zhihua Chen +3 more
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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
Chenkuan Li +3 more
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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
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Integral Representation of the Mittag-Leffler Function
Russian Mathematics, 2022 Generalization of the integral representation of the gamma function has been obtained, which shows that the Hankel contour assumes rotation in the complex plane. The range of admissible values for the contour rotation angle is set. Using this integral representation, generalization of the integral representation of the Mittag-Leffler function has been ...
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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 +3 more
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Journal of Inequalities and Applications, 2018 In this paper we prove the Hadamard and the Fejér–Hadamard inequalities for the extended generalized fractional integral operator involving the extended generalized Mittag-Leffler function.
Shin Min Kang +3 more
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On Modifications of the Gamma Function by Using Mittag-Leffler Function
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
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A Comprehensive Study on the Zeros of the Two-Parameter Mittag-Leffler Function [PDF]
Sahand Communications in Mathematical AnalysisThe Mittag-Leffler function appears as an analytical solution of some fractional differential equations. The behavior of the zeros of the Mittag-Leffler function, especially their asymptotic distribution, plays a fundamental role in the study of ...
Farnoosh Abooali +1 more
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