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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512060

Digital Object Identifier
doi:10.1155/2013/493164

Mathematical Reviews number (MathSciNet)
MR3108637

Zentralblatt MATH identifier
1291.34014

Citation

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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