We study the combined effects of noise and detector sensitivity on a dynamical process that generates intermittent events mimicking the behavior of complex systems. By varying the sensitivity level of the detector we move between two forms of complexity, from inverse power law to Mittag-Leffler interevent time survival probabilities. Here fluctuations fight against complexity, causing an expone...

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 zero distribution of sections of Mittag–Leffler functions of order ρ > 1 was studied in 1983 by A. Edrei, E.B. Saff and R.S. Varga. In the present paper, we study the zero distribution of linear combinations of sections and tails of Mittag–Leffler functions of order ρ > 1.

1050 NOTICES OF THE AMS VOLUME 46, NUMBER 9 T his year marks the thirtieth anniversary of the realization of the dream of one Swedish mathematician. In 1916, on his seventieth birthday, Gösta Mittag-Leffler promised his and his wife’s considerable fortune to the goal of founding a mathematics institute. More than forty years had to pass after his death before the institute was launched in earne...

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) ∫ ...

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy alpha -stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler...

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...

This paper introduces techniques for the estimation of solutions to fractional order differential equations (FODEs) and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces (RKHSs). Specifically, an RKHS is generated for the purpose of estimating fractional derivatives from the Mittag-Lef...

This paper addresses the problem of the numerical computation of generalized Mittag–Leffler functions with two parameters, with applications in fractional calculus. The inversion of their Laplace transform is an effective tool in this direction; however, the choice of the integration contour is crucial. Here parabolic contours are investigated and combined with quadrature rules for the numerica...