Mixed monotone operator methods for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems
School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi, 030006, P.R. China
Boundary Value Problems 2013, 2013:85 doi:10.1186/1687-2770-2013-85Published: 10 April 2013
This work is concerned with the existence and uniqueness of positive solutions for the following fractional boundary value problem:
where is the standard Riemann-Liouville fractional derivative of order ν, and , . Our analysis relies on two new fixed point theorems for mixed monotone operators with perturbation. Our results can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate the main result.
MSC: 26A33, 34B18, 34B27.