Abstract We present unified versions of Minkowski-type fractional integral inequalities with the help operator based on a Mittag-Leffler function. These provide new as well already known inequalities.

In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This Mittag-Leffler function distribution (MLFD) belongs to the generalized hypergeometric and generalized power series families and also arises as weighted Poisson...

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...

Abstract In this paper, we introduce a new integral transform, namely Aboodh and apply the transform to investigate Hyers–Ulam stability, Hyers–Ulam–Rassias Mittag-Leffler–Hyers–Ulam Mittag-Leffler–Hyers–Ulam–Rassias stability of second order linear differential equations.

This paper deals with a new mathematical model of the hamstring muscle group. The proposed viscoelastic model includes fractional derivatives of stretching force and elongation as well as restrictions on the coefficients that follow from the second law of thermodynamics. On the basis of experimental data four coefficients of the model have been calculated by numerical procedure. Obtained result...

We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z , where z is a complex variable satisfying 0 arg z 2 π . A summary of the asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using the method of steepest descents ...

In this paper we study the class of mixed-index time fractional differential equations in 1 which different components of the problem have different time fractional derivatives on the left hand 2 side. We prove a theorem on the solution of the linear system of equations, which collapses to the 3 well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the 4 ...

In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...