On existence theorems of a functional differential equations in partially ordered Banach algebras

TL;DR

This paper establishes existence theorems for coupled quadratic functional differential equations by applying fixed point theorems in partially ordered Banach algebras, providing a new approach to such problems.

Contribution

It introduces fixed point theorems of Dhage's type for block operator matrices in partially ordered Banach algebras to prove existence results.

Findings

Existence results for coupled quadratic functional differential equations.

Application of fixed point theorems in partially ordered Banach algebras.

Reduction of the system to a fixed point problem for a block operator matrix.

Abstract

In this paper we are concerned with existence results for a coupled system of quadratic functional differential equations. This system is reduced to a fixed point problem for a block operator matrix with nonlinear inputs. To prove the existence we are established some fixed point theorem of Dhage's type for the block matrix operator acting in partially ordered Banach algebras.