Rheological behavior of certain non–Newtonian fluids in engineering sciences is often modeled by power law ansatzes with p ≤ 2. So far, existing numerical analysis for local strong solutions study a fully implicit time discretization and find only restricted ranges of admissible p’s for corresponding error estimates [9]; different nonlinear stabilization strategies which allow a corresponding e...

We consider an inverse problem arising from an time-dependent driftdiffusion model in semiconductor devices, which is formulated in terms of a system of parabolic equations for the electron and hole densities and the Poisson equation for the electric potential. This inverse problem aims to identify the doping profile from the final overdetermination data of the electric potential. By using the ...

This work deals with a new finite time stability (FTS) of neutral fractional order systems delay (NFOTSs). In light this, FTSs NFOTSs are demonstrated in the literature using Gronwall inequality. The innovative aspect our proposed study is application fixed point theory to show FTS NFOTSs. Finally, two examples, theoretical contributions confirmed and substantiated.

This paper is concerned with the tempered pullback dynamics of 2D Navier-Stokes equations sublinear time delay operators subject to non-homogeneous boundary conditions in Lipschitz-like domains. By virtue estimates background flow domain and a new retarded Gronwall inequality, we establish existence attractors general setting involving universes.

The classical Gronwall inequality is one of the basic tools in theory differential and integral equations. In this paper, a new version presented extended to equations with generalized Hattaf fractional derivative involving non-singular kernel. existence uniqueness solutions for such last type are rigorously investigated. Furthermore, an application study Ulam-Hyers stability certain

We prove the existence of multiple positive solutions nonlinear second-order nonlocal boundary value problems with term having derivative dependence. allow nonlinearity to grow quadratically respect derivatives. obtain a priori bounds for norms derivatives by using recently obtained Gronwall-type inequality. Three examples illustrate some results. This article is part theme issue ‘Topological d...

In this paper, we derive the representation formula of solution for ?-Hilfer fractional differential equation with constant coefficient in form Mittag-Leffler function by using Picard’s successive approximation. Moreover, some properties and fixed point theorems such as Banach Schaefer, introduce new results qualitative existence uniqueness. The generalized Gronwall inequality lemma is used ana...