Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

الملخص EN

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.