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Zbl 1219.34005
Al-Refai, Mohammed; Hajji, Mohamed Ali
Monotone iterative sequences for nonlinear boundary value problems of fractional order. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 11, 3531-3539 (2011). ISSN 0362-546X

Summary: 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.

MSC 2000:: *34A08
34B15 Nonlinear boundary value problems of ODE
34B18 Positive solutions of nonlinear boundary value problems
34A45 Theoretical approximation of solutions of ODE

Keywords: fractional differential equations; boundary value problems; maximum principle; lower and upper solutions; Caputo fractional derivative

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