Monotone Iterative Method for a Class of Nonlinear Fractional Differential Equations

Abstract

By applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D (q) x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.