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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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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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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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Some new applications of the fractional integral and four-parameter Mittag-Leffler function. [PDF]
PLoS OneThe article reveals new applications of the four-parameter Mittag-Leffler function (MLF) in geometric function theory (GFT), using fractional calculus notions.
Abubaker AA +3 more
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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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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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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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Fractal and Fractional, 2021 This article uses fractional calculus to create novel links between the well-known Mittag-Leffler functions of one, two, three, and four parameters.
F. Ghanim +2 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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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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