Ulam‐type stability for differential equations driven by measures

Abstract

Based on a notion of Stieltjes derivative of a function with respect to another function, we provide Ulam–Hyers type stability results for nonlinear differential equations driven by measures on compact or on unbounded intervals, in the lack of Lipschitz continuity assumptions. In particular, one can deduce stability results for generalized differential equations, dynamic equations on time scales or impulsive differential equations (including the case of an infinite number of impulses that accumulate in the considered interval, thus allowing the study of Zeno hybrid systems).

Hyers–Ulam Stability and Existence of Solutions to the Generalized Liouville–Caputo Fractional Differential Equations

“…Hyers-Ulam stability has been one of the most active research topics in differential equations, and obtained a series of results (see [21][22][23][24][25][26][27][28][29][30]). Recently, Alqifiary et al [22] obtained generalized Hyers-Ulam stability of linear differential equations.…”

Hyers–Ulam Stability for Cayley Quantum Equations and Its Application to h-Difference Equations

“…Implicit fractional q-difference equations are treated by [1,2,10]. Fractional stability is investigated by [7] and [20], time-dependent and periodic coefficients by [9], and differential equations and HUS driven by measures is the focus of [19].…”

On coupled nonlinear evolution system of fractional order with a proportional delay

“…One of the features is UH-type stability that got significant attention from the researchers. 30,31 After some modifications in UH-type stability, the researchers applied it to different systems in a successful way to gain the desired results (we refer several studies [32][33][34][35][36][37] ).…”