Abstract The main aim of this article is to study a new generalizations the Gauss hypergeometric matrix and confluent functions by using two-parameter Mittag–Leffler function. In particular, we investigate certain important properties these extended such as integral representations, differentiation formulas, beta transform, Laplace transform. Furthermore, introduce an extension Jacobi orthogona...

Abstract In this paper, we propose a generalized Gronwall inequality in the context of ψ -Hilfer proportional fractional derivative. Using Picard’s successive approximation and definition Mittag–Leffler functions, construct representation formula solution for differential equation with constant coefficient form kernel. The uniqueness result is proved by using Banach’s fixed-point theorem some p...

The problem of calculating the Mittag-Leffler function Eρ,μ(z) is considered in paper. To solve this integral representations for are transformed such a way that they could not contain complex variables and parameters. Integral written form allow one to use standard methods numerical integration calculate integrals contained them. verify correctness obtained was calculated both with formulas kn...

Generalization of the integral representation gamma function has been obtained, which shows that Hankel contour assumes rotation in complex plane. The range admissible values for angle is set. Using this representation, generalization Mittag-Leffler obtained expresses value terms integral.

*Correspondence: [email protected]; [email protected] 1Department of Applied Mathematics, Yanshan University, Qinhuangdao, 066001, China Full list of author information is available at the end of the article Abstract This paper is concerned with the global projective synchronization issue for fractional neural networks in the Mittag-Leffler stability sense. Firstly, a fractional-order differ...