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Zbl 1222.65078
Al-Mdallal, Qasem M.; Syam, Muhammed I.; Anwar, M.N.
A collocation-shooting method for solving fractional boundary value problems. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 15, No. 12, 3814-3822 (2010). ISSN 1007-5704

Summary: We discuss the numerical solution of special class of fractional boundary value problems of order $2$. The method of solution is based on a conjugating collocation and spline analysis combined with shooting method. A theoretical analysis about the existence and uniqueness of exact solution for the present class is proved. Two examples involving Bagley-Torvik equation subject to boundary conditions are also presented; numerical results illustrate the accuracy of the present scheme.

MSC 2000:: *65L60 Finite numerical methods for ODE
34A08
26A33 Fractional derivatives and integrals (real functions)
45J05 Integro-ordinary differential equations

Keywords: collocation method; shooting method; Bagley-Torvik equation

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Zentralblatt MATH Berlin [Germany]