Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 493164, 8 pages.
Monotone Iterative Solutions for Nonlinear Boundary Value Problems of Fractional Differential Equation
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.
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