HYERS-ULAM STABILITY FOR NONLOCAL DIFFERENTIAL EQUATIONS

DOI: 10.18173/2354-1059.2020-0041

Abstract

In this paper, we present a result on Hyers-Ulam stability for a class of nonlocal differential equations in Hilbert spaces by using the theory of integral equations with completely positive kernels together with a new Gronwall inequality type. The paper develops some recent results on fractional differential equations to the ones involving general nonlocal derivatives. Instead of Mittag-Leffler functions, we must utilize the characterization of relaxation function.