Monotone iterative sequences for nonlinear boundary value problems of fractional order

Mohammed Al-Refai, Mohamed Ali Hajji

Research output: Contribution to journalArticlepeer-review

76 Citations (Scopus)

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 languageEnglish
Pages (from-to)3531-3539
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number11
DOIs
Publication statusPublished - Jul 1 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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