Some New Fractional-Calculus Connections between Mittag–Leffler Functions

By Hari M. Srivastava, Arran Fernandez, Dumitru Băleanu. Mathematics, 2019

55 citations recorded by the source corpus.

We consider the well-known Mittag–Leffler functions of one, two and three parameters, and establish some new connections between them using fractional calculus. In particular, we express the three-parameter Mittag–Leffler function as a fractional derivative of the two-parameter Mittag–Leffler function, which is in turn a fractional integral of the one-parameter Mittag–Leffler function. Hence, we derive an integral expression for the three-parameter one in terms of the one-parameter one. We discuss the importance and applications of all three Mittag–Leffler functions, with a view to potential applications of our results in making certain types of experimental data much easier to analyse.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/b391163752de852c8aca77c14f334b989bdb59d3

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

On Fractional Operators and Their Classifications (2019, methodology): “• A model due to Prabhakar [40], which was formally connected to fractional calculus in [41] and whose applications have been discussed in [42,43], utilises an integral transform with a three-parameter Mittag-Leffler function (E μ,ν(z) = ∑n=0 (ρ)nz Γ(nμ+ν) for Re(μ), Re(ν) > 0) in the kernel:”