By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann-Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in Al-Refai (2012). As applications, an example is presented to illustrate our main results.
Wenzhe Xie. Jing Xiao. Zhiguo Luo. "Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem." Abstr. Appl. Anal. 2014 (SI40) 1 - 9, 2014. https://doi.org/10.1155/2014/540351