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
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A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function☆ [PDF]
Alexandria Engineering Journal, 2022 The aim of this paper is to present and analyze the fractional optimal control model for COVID-19 and diabetes co-dynamics, using the Atangana-Baleanu derivative.
Omame A +3 more
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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 +3 more
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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 ...
Shilpi Jain +3 more
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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
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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
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A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators [PDF]
Computational and Applied Mathematics, 2020 We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional integral ...
A. Fernandez +2 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 of the
Dinesh Kumar, Jeta Ram, Junesang Choi
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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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The Prabhakar or three parameter Mittag-Leffler function: Theory and application [PDF]
Communications in nonlinear science & numerical simulation, 2017 The Prabhakar function (namely, a three parameter Mittag–Leffler function) is investigated. This function plays a fundamental role in the description of the anomalous dielectric properties in disordered materials and heterogeneous systems manifesting ...
R. Garra, R. Garrappa
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