A remarkably large number of unified integrals involving the Mittag–Leffler function have been presented. Here, with same technique as Choi and Agarwal, we propose establishment two generalized integral formulas a multivariate function, which are expressed in terms Lauricella series due to Srivastava Daoust. We also present some interesting special cases.

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.

*Correspondence: [email protected] 2College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China 3Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, 710049, China Full list of author information is available at the end of the article Abstract This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg ...

Linear operators which (1) preserve the reality of zeros of polynomials having only real zeros and (2) map stable polynomials into stable polynomials are investigated using recently established results concerning the zeros of certain Fox–Wright functions and generalized Mittag-Leffler functions. The paper includes several open problems and questions.  2005 Elsevier Inc. All rights reserved.

*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...

In this paper, the Kharrat–Toma transforms of Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and regularized version HP derivative are derived. Moreover, we also compute solution some Cauchy problems diffusion equations modeled with via transform. The solutions computed in form generalized Mittag–Leffler function.

Abstract This paper addresses the asymptotic behavior of systems described by nonlinear differential equations with two fractional derivatives. Using Mittag–Leffler function, Laplace transform, and generalized Gronwall inequality, a sufficient stability condition is derived for such systems. Numerical examples illustrate theoretical results.

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 ...

As well-known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus the interest on some new aspects of the dynamics, successively considering the memory kernel, the particle’s mean velocity, and the scattering function. All these quantities are studied from a un...