Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System

Boundary value problems

Yuming Chen¹  Zigen Ouyang²  Shuliang Zou³ 

[1] Department of Mathematics, Wilfrid Laurier University, Waterloo, Canada;School of Mathematics and Physics, School of Nuclear Science and Technology, University of South China, Hengyang, China;School of Nuclear Science and Technology, University of South China, Hengyang, China

关键词: Ordinary Differential Equation;    Fractional Order;    Fractional Derivative;    Fixed Point Theorem;    Fractional Differential Equation;   

DOI  :  10.1155/2011/475126

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Though boundary value problems for fractional differential equations have been extensively studied, most of the studies focus on scalar equations and the fractional order between 1 and 2. On the other hand, delay is natural in practical systems. However, not much has been done for fractional differential equations with delays. Therefore, in this paper, we consider a boundary value problem of a general delayed nonlinear fractional system. With the help of some fixed point theorems and the properties of the Green function, we establish several sets of sufficient conditions on the existence of positive solutions. The obtained results extend and include some existing ones and are illustrated with some examples for their feasibility.

【 授权许可】

CC BY