Anti-periodic fractional boundary value problems for nonlinear differential equations of fractional order

Fang Wang,Zhenhai Liu

doi:10.1186/1687-1847-2012-116

Abstract

By using Schauder’s fixed point theorem and the contraction mapping principle, we discuss the existence of solutions for nonlinear fractional differential equations with fractional anti-periodic boundary conditions. Some examples are given to illustrate the main results.

Highlights

Fractional calculus has been recognized as an effective modeling methodology by researchers
Second and higher-order differential equations with anti-periodic boundary value conditions have been considered in papers [ – ]
We investigate the existence and uniqueness of solutions for an antiperiodic fractional boundary value problem given by

Summary

Introduction

Fractional calculus has been recognized as an effective modeling methodology by researchers. Fractional differential equations are generalizations of classical differential equations to an arbitrary order. They have broad application in engineering and sciences such as physics, mechanics, chemistry, economics and biology, etc. There has been a great deal of research into the questions of existence and uniqueness of solutions to anti-periodic boundary value problems for differential equations. Second and higher-order differential equations with anti-periodic boundary value conditions have been considered in papers [ – ]. The existence of solutions for anti-periodic boundary value problems for fractional differential equations was studied in [ – ]. We investigate the existence and uniqueness of solutions for an antiperiodic fractional boundary value problem given by.

Main results

Examples