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.

The objective of this paper is to establish some new refinements of fractional Hermite-Hadamard inequalities via a harmonically convex function with a kernel containing the generalized Mittag-Leffler function.

*Correspondence: [email protected] School of Mathematical Science, Anhui University, Hefei, P.R. China Abstract In this paper, using the theory of q-fractional calculus, we deal with the q-Mittag-Leffler stability of q-fractional differential systems, and based on it, we analyze the direct Lyapunov method of q-fractional differential systems. Several sufficient criteria are established to guaran...

Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward ...

After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each oth...

In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show tha...

In this paper, a mathematical model containing two-parameter Mittag-Leffler function in its definition is proposed to be used for the first time to fit the relation between unemployment rate and inflation rate, also known as the Phillips curve. The Phillips curve is in the literature often represented by an exponential-like shape. On the other hand, Phillips in his fundamental paper used a powe...

Stability is the most relevant property of dynamical systems. The stability stochastic differential equations a challenging and still open problem. In this article, using fuzzy Mittag–Leffler function, we introduce new controller function to stabilize equation (SDE) ν′(γ,μ)=Fγ,μ,ν(γ,μ). By adopting fixed point technique, are able prove Mittag–Leffler–Hyers–Ulam–Rassias SDE.