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Fractional boundary value problems: analysis and numerical methods. (English) Zbl 1273.65098
Summary: We consider nonlinear boundary value problems for differential equations of fractional order \(\alpha\), \(0 < \alpha < 1\). We study the existence and uniqueness of the solution and extend existing published results. In the last part of the paper we study a class of prototype methods to determine their numerical solution.

MSC:
65L05 Numerical methods for initial value problems
34A08 Fractional ordinary differential equations and fractional differential inclusions
45J05 Integro-ordinary differential equations
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