Existence Results for a Coupled System of Nonlinear Fractional Differential Equation with Four-Point Boundary Conditions

M Gaber,M G Brikaa

doi:10.5402/2011/468346

Abstract

This paper studies a coupled system of nonlinear fractional differential equation with four-point boundary conditions. Applying the Schauder fixed-point theorem, an existence result is proved for the following system: , , , , , , , , where satisfy certain conditions.

Highlights

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymerrheology, and so forth involves derivatives of fractional order
The study of coupled systems involving fractional differential equations is important as such systems occur in various problems of applied nature, for instance, see 9, 10
In 11, the existence of nontrivial solutions was investigated for a coupled system of nonlinear fractional differential equations with two-point boundary conditions by using Schauder’s fixed-point theorem

Summary

Introduction

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modelling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymerrheology, and so forth involves derivatives of fractional order. In 11 , the existence of nontrivial solutions was investigated for a coupled system of nonlinear fractional differential equations with two-point boundary conditions by using Schauder’s fixed-point theorem. The existence of nontrivial solutions for a coupled system of nonlinear fractional differential equations with

Results

Conclusion