Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840873 | Nonlinear Analysis: Theory, Methods & Applications | 2011 | 9 Pages |
Abstract
In this paper we extend the maximum principle and the method of upper and lower solutions to boundary value problems with the Caputo fractional derivative. We establish positivity and uniqueness results for the problem. We then introduce two well-defined monotone sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. A numerical iterative scheme is introduced to obtain an accurate approximate solution for the problem. The accuracy and efficiency of the new approach are tested through two examples.
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Authors
Mohammed Al-Refai, Mohamed Ali Hajji,