Abstract and Applied Analysis

Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation

Chaozhu Hu, Bin Liu, and Songfa Xie

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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.

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Abstr. Appl. Anal., Volume 2013 (2013), Article ID 493164, 8 pages.

First available in Project Euclid: 27 February 2014

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Hu, Chaozhu; Liu, Bin; Xie, Songfa. Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation. Abstr. Appl. Anal. 2013 (2013), Article ID 493164, 8 pages. doi:10.1155/2013/493164. https://projecteuclid.org/euclid.aaa/1393512060

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