Existence results for integro-differential equations with reflection

TL;DR

This paper establishes existence and uniqueness of pseudo almost automorphic solutions with measure for certain integro-differential equations with reflection, using fixed point theory and properties of almost automorphic functions.

Contribution

It introduces new existence and uniqueness results for integro-differential equations with reflection involving pseudo almost automorphic solutions with measure.

Findings

Proves existence and uniqueness of solutions.

Analyzes linear and nonlinear cases.

Provides illustrative example.

Abstract

We prove several important results concerning existence and uniqueness of pseudo almost automorphic (paa) solutions with measure for integro-differential equations with reflection. We use the properties of almost automorphic functions with measure and the Banach fixed point theorem, and we discuss two linear and nonlinear cases. We conclude with an example and some observations.