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On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function
Mathematics, 2022 The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded.
M. Samraiz +5 more
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On complete monotonicity of three parameter Mittag-Leffler function
Applicable Analysis and Discrete Mathematics, 2021 Using the Bernstein theorem we prove the complete monotonicity of the three parameter Mittag?Leffler function E??,? (?w) for w ? 0 and suitably constrained parameters ?, ? and ?.
K. Górska +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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On a Five-Parameter Mittag-Leffler Function and the Corresponding Bivariate Fractional Operators
Fractal and Fractional, 2021 Several extensions of the classical Mittag-Leffler function, including multi-parameter and multivariate versions, have been used to define fractional integral and derivative operators.
M. A. Özarslan, A. Fernandez
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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 +3 more
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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
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Boundary Value Problems, 2023 Introducing a new generalized multivariate Mittag-Leffler function which is a generalization of the multivariate Mittag-Leffler function, we derive a sufficient condition for the uniqueness of solutions to a brand new boundary value problem of the ...
Chenkuan Li +3 more
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Some New Fractional-Calculus Connections between Mittag–Leffler Functions
Mathematics, 2019 We consider the well-known Mittag−Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus.
Hari M. Srivastava +2 more
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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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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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