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...

Abstract This study is aimed to investigate the sufficient conditions of existence unique solutions and Ulam–Hyers–Mittag-Leffler (UHML) stability for a tripled system weighted generalized Caputo fractional derivatives investigated by Jarad et al. (Fractals 28:2040011 2020) in frame Chebyshev Bielecki norms with time delay. The acquired results are obtained using Banach fixed point theorems Pic...

A new time-fractional derivative with Mittag-Leffler memory kernel, called the generalized Atangana-Baleanu is defined along associated integral operator. Some properties of operators are proved. The operator suitable to generate by particularization known Atangana-Baleanu, Caputo-Fabrizio and Caputo derivatives. mathematical model advection-dispersion process kinetic adsorption formulated cons...

Symmetry is a fascinating property of numerous mathematical notions. In analysis function f:[a,b]→R symmetric about a+b2 satisfies the equation f(a+b−x)=f(x). this paper, we investigate relationship unified Mittag–Leffler with some known special functions. We have obtained integral transforms in terms Wright generalized function. also established recurrence relation along another important resu...

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...