Stability in nonlinear integro-differential equations with functional delay on Time scale

Abstract

The main purpose of this work is to show the stability of the zero solution for a non-linear neutral differential equation on space called the Time scale. In order to achieve our purposes, we assume a time scale , that is unbounded above and below, and we employ the contractive mapping theorem by converting the neutral differential equation into an equivalent integral equation,  which allows us to reach the desired result of the asymptotic stability of the zero solution on Time scale provided that