On Dynamic Equation in Banach Space of Continuous Functions in Time Scale

Abstract

We investigate existence of solution of local dynamic initial value problem in the Banach space of continuous function from an interval in time scale to an arbitrary Banach space. We use the concept of measure of noncompactness and Meir-Keeler condensing operator involving $L$-function to obtain the existence of solutions of the problem. We also give an example to illustrate our result.