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...

The paper is oriented on the existence of almost periodic solutions factional-order impulsive delayed reaction-diffusion gene regulatory networks. Caputo type fractional-order derivatives and disturbances at not fixed instants time are considered. New perfect Mittag–Leffler stability criteria proposed. Lyapunov’s like functions, properties fractional comparison principle main tools in investiga...

In this paper, we present a new result that allows for studying the global stability of disease-free equilibrium point when basic reproduction number is less than 1, in fractional calculus context. The method only involves linear algebra and can be easily applied to study asymptotic stability. After proving some auxiliary lemmas involving Mittag–Leffler function, main paper. Under assumptions, ...

The main goal of the paper is to use a generalized proportional Riemann–Liouville fractional derivative (GPRLFD) model BAM neural networks and study some stability properties equilibrium. Initially, several GPRLFD are proved, such as squared function. Additionally, comparison results for provided. Two types equilibrium with defined. In connection applied its singularity at initial time, Mittag-...

Stability analysis over a finite time interval is well-formulated technique to study the dynamical behaviour of system. This article provides novel on finite-time stability fractional-order system using approach delayed-type matrix Mittag-Leffler function. At first, we discuss solution’s existence and uniqueness for our considered fractional model. Then standard form integral inequality Gronwal...