Analysis of Volterra Integrodifferential Equations with Nonlocal and Boundary Conditions via Picard Operator

TL;DR

This paper studies the existence, uniqueness, and dependency of solutions for second-order Volterra integrodifferential equations with nonlocal and boundary conditions using fixed point and Picard operator theories.

Contribution

It introduces a new approach to analyze solutions of complex integrodifferential equations with nonlocal boundary conditions via Picard operators.

Findings

Established conditions for existence and uniqueness of solutions.

Analyzed how solutions depend on initial nonlocal data.

Applied fixed point theory to integrodifferential equations.

Abstract

This article investigates the existence and uniqueness of solutions to the second order Volterra integrodifferential equations with nonlocal and boundary conditions through its integral equivalent equations and fixed point of Banach. Further, utilising the Picard operator theory we obtain the dependency of solutions on the initial nonlocal data and on functions involved on the right hand side of the equations.