The Mittag-Leffler (ML) function plays a fundamental role in fractional calculus but very few methods are available for its numerical evaluation. In this work we present a method for the efficient computation of the ML function based on the numerical inversion of its Laplace transform (LT): an optimal parabolic contour is selected on the basis of the distance and the strength of the singulariti...

In this communique, we present a new family of Nussbaum functions expressed by Mittag–Leffler functions under certain conditions. © 2009 Elsevier Ltd. All rights reserved.

In this paper, we show several Turán type inequalities for a generalized Mittag-Leffler function with four parameters via the [Formula: see text]-gamma function.

The main object of this paper is to investigate the solution of the following free electron laser equations associated with generalized MittagLeffler function and a confluent hypergeometric function in two variables: Dα τ h(τ) = ω ∫ τ 0 t β−1 h(τ − t)E σ,β(iνt σ)dt+ δf(τ), where γ, δ, ω ∈ C; ν ∈ R,α > 0, σ > 0, β > 0; E σ,β(z) is the generalized Mittag-Leffler function and Dα τ h(τ) = λ Γ(γ) ∫ ...

The generalized Mittag-Leffler function Eα,β (z) has been studied for arbitrary complex argument z ∈ C and parameters α ∈ R+ and β ∈ R. This function plays a fundamental role in the theory of fractional differential equations and numerous applications in physics. The Mittag-Leffler function interpolates smoothly between exponential and algebraic functional behaviour. A numerical algorithm for i...

A new type of an integrable mapping is presented. This map is equipped with fractional difference and possesses an exact solution, which can be regarded as a discrete analogue of the Mittag-Leffler function.

The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space R+. Some properties are given and, in particular, we prove a long-range dependence property.