Green’s function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application

Jie Zhou,Meiqiang Feng

doi:10.1186/1687-2770-2014-69

Abstract

In this paper, we discuss the expression and properties of Green’s function for boundary value problems of nonlinear Sturm-Liouville-type fractional order impulsive differential equations. Its applications are also given. Our results are compared with some recent results by Bai and Lu.

Highlights

1 Introduction Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, Bode’s analysis of feedback amplifiers, capacitor theory, electrical circuits, electron-analytical chemistry, biology, control theory, fitting of experimental data, and so forth, and involves derivatives of fractional order
Fractional derivatives provide an excellent tool for the description of memory and hereditary properties of various materials and processes. This is the main advantage of fractional differential equations in comparison with classical integer-order models
In this paper, we shall study the expression of the solution of fractional impulsive differential equations by using Green’s function

Summary

Introduction

Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of complex medium, polymer rheology, Bode’s analysis of feedback amplifiers, capacitor theory, electrical circuits, electron-analytical chemistry, biology, control theory, fitting of experimental data, and so forth, and involves derivatives of fractional order. The boundary value problems of impulsive differential equations of integer order have been studied extensively in the literature (see [ – ]). The theory using Green’s function to express the solution of fractional impulsive differential equations has not been investigated till now. In this paper, we shall study the expression of the solution of fractional impulsive differential equations by using Green’s function.

Results

Conclusion