Existence of Positive Solutions to a Boundary Value Problem for a Delayed Nonlinear Fractional Differential System
1 School of Mathematics and Physics, School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
2 Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada, N2L 3C5
3 School of Nuclear Science and Technology, University of South China, Hengyang 421001, China
Boundary Value Problems 2011, 2011:475126 doi:10.1155/2011/475126Published: 14 March 2011
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.