The paper is devoted to the study of subdiffusion equations with Mittag-Leffler nonlinearity. The comparison principle proved in a bounded domain. results on local existence, global and blow-up solutions initial-boundary value problem are obtained. In addition, existence initial whole Euclidean space proven.

The paper is devoted to study analogues of the van der Corput lemmas involving Mittag-Leffler functions. generalisation that we replace exponential function with Mittag-Leffler-type function, oscillatory integrals appearing in analysis time-fractional partial differential equations. More specifically, integral form I?,?(?)=?RE?,?(i???(x))?(x)dx, for range 00. This extends variety estimat...

We consider here the recently proposed closed-form formula in terms of the Meijer G functions for the probability density functions g(α)(x) of one-sided Lévy stable distributions with rational index α=l/k, with 0<α<1. Since one-sided Lévy and Mittag-Leffler distributions are known to be related, this formula could also be useful for calculating the probability density functions ρ(α)(x) of the l...

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...

A partial order is defined on partitions by the removal of rim hooks of a given length. This poset is isomorphic to a product of Young lattices, guaranteeing rim hook versions of Schensted correspondences. Analogous results are given for shifted shapes. 1. Main Results A shape (Young diagram) is a finite order ideal of the lattice P = {(k, l) : k, l ≥ 1}. Shapes form the so-called Young lattice...

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...