A new generalization of the Katugampola generalized fractional integrals in terms Mittag-Leffler functions is proposed. Consequently, generalizations Hermite-Hadamard inequalities by this newly proposed integral operator, for a positive convex stochastic process, are established. Other known results easily deduced as particular cases these inequalities. The obtained also hold any function.

We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...

The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are presented in a compact and elegant form in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for numerical computation...

Abstract. This paper deals with the study of the generalized hypergeometric matrix function and obtains some of its properties. We rephrase some results from the previous (earlier) works that will be used in this study. We get the hypergeometric matrix function representation, matrix differential equation, generating matrix functions, bilinear generating matrix functions, matrix recurrence rela...

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...

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...