By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.
"Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation." Abstr. Appl. Anal. 2013 1 - 8, 2013. https://doi.org/10.1155/2013/493164