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.
| Original language | English |
|---|---|
| Pages (from-to) | 3531-3539 |
| Number of pages | 9 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 74 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - Jul 2011 |
Keywords
- Boundary value problems
- Caputo fractional derivative
- Fractional differential equations
- Lower and upper solutions
- Maximum principle
ASJC Scopus subject areas
- Analysis
- Applied Mathematics
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