Extremal solutions of nonlinear functional discontinuous fractional equations

Abstract

This paper is devoted to prove the existence of extremal solutions of Fractional equation with Riemann-Liouville derivative. The existence follows from the method of lower and upper solutions. Some jumps in the derivative of these functions are allowed. It is important to point out that a discontinuous and functional dependence on the nonlinear part of the equation with respect to the solution is allowed. The construction of the Green’s function related to the linear part of the equation coupled to spectral theory is fundamental to deduce the results.