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Monotone iterative sequences for nonlinear boundary value problems of fractional order. (English) Zbl 1219.34005
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:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
34A45Theoretical approximation of solutions of ODE
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