Positive solutions of Riemann-Stieltjes integral boundary problems for the nonlinear coupling system involving fractional-order differential

Kaihong Zhao,Ping Gong

doi:10.1186/1687-1847-2014-254

Abstract

In this article, we study Riemann-Stieltjes integral boundary value problems of nonlinear fractional functional differential coupling system involving higher-order Caputo fractional derivatives. Some sufficient criteria are obtained for the existence, multiplicity, and nonexistence of positive solutions by applying fixed-point theorems on a convex cone. As applications, some examples are provided to illustrate our main results.

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
This is the main advantage of fractional differential equations in comparison with classical integer-order models
The boundary value problems with Riemann-Stieltjes integral boundary condition arise in a variety of different areas of applied mathematics and physics

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. There have been many papers focused on boundary value problems of fractional ordinary differential equations (see [ – ]). Nonlocal boundary value problems of fractional-order differential equations constitute a class of very interesting and important problems. To the best of our knowledge, there are only few papers dealing with the existence, multiplicity, and nonexistence of positive solutions of RiemannStieltjes integral boundary problems for high-order nonlinear fractional differential coupling system.

Results

Conclusion