Well-Posedness of some nonlinear Volterra-Fredholm integral and integro-dynamic equations on time scales

TL;DR

This paper investigates the well-posedness of nonlinear Volterra-Fredholm integral and integro-dynamic equations on arbitrary time scales, extending classical results to a unified time scale framework using integral inequalities and fixed-point theory.

Contribution

It introduces a time scale analogue of Pachpatte-type integral inequalities and applies them to prove existence and uniqueness of solutions for these equations.

Findings

Established well-posedness results on unbounded intervals

Derived new integral inequalities of Pachpatte type on time scales

Applied fixed-point theorem to nonlinear dynamic equations

Abstract

In this paper we study well posedness of a certain nonlinear Volterra-Fredholm dynamic integral and integro-dynamic equations on unbounded interval from arbitrary time scale. We derive the time scale analogue of certain integral inequalities of Pachpatte type and using them with Banach's fixed-point theorem to establish the results.