In 1986, Dixon and McKee (Z Angew Math Mech 66:535–544, 1986) developed a discrete fractional Gronwall inequality, which can be seen as generalization of the classical inequality. However, this generalized inequality its variant (Al-Maskari Karaa in SIAM J Numer Anal 57:1524–1544, 2019) have not been widely applied numerical analysis time-stepping methods for time-fractional evolution equations...

Abstract This work is mainly concentrated on finite-time stability of multiterm fractional system for $0 < \alpha _{2} \leq 1 _{1} 2$ 0 < ? 2 ? 1 with multistate time delay. Considering the Caputo...

Abstract In this paper, we propose a generalized Gronwall inequality in the context of ψ -Hilfer proportional fractional derivative. Using Picard’s successive approximation and definition Mittag–Leffler functions, construct representation formula solution for differential equation with constant coefficient form kernel. The uniqueness result is proved by using Banach’s fixed-point theorem some p...

In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound third-order derivative term, and theory fixed-point index used suitable open sets obtain existence positive solutions. The have quadratic growth te...

Abstract We give a rigorous derivation of the incompressible 2D Euler equation from von Neumann with an external magnetic field. The convergence is respect to modulated energy functional, and implies weak in sense measures. This semi-classical counterpart theorem 1.5 (Han-Kwan Iacobelli Proc Am Math Soc 149(7):3045–3061, 2021). Our proof based on Gronwall estimate for which turn heavily relies ...

This paper is concerned with the asymptotic stability derived for two-dimensional incompressible Navier–Stokes equations multidelays on Lipschitz domain, which models control theory of 2D fluid flow. By a new retarded Gronwall inequality and estimates stream function Stokes equations, complete trajectories inside pullback attractors are asymptotically stable via restriction generalized Grashof ...