Basics of Volterra integral equations on time scales

Abstract

This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this subject, we can replace continuity property of the kernel function with the weaker one rd-continuity. The paper also covers results concerning the following concepts: The notion of resolvent kernel, and its role in formulation of the solution, the reciprocity property of kernels, Piccard iterates, relation between linear dynamic equations and Volterra integral equations, some special type of kernels together with several illustrative examples.