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On the numerical solution of fractional Sturm-Liouville problems. (English) Zbl 1202.65100
Summary: The differential equation of Sturm-Liouville problems is generalized into fractional form by replacing the first-order derivative by a fractional derivative of order α,0<α1. We show briefly that this class of eigenvalue problems could be very promising to the solution of linear fractional partial differential equations. The homotopy perturbation method is considered for computing the eigenelements of the present problem. Based on our simulations some theoretical conjectures are reported.
MSC:
65L15Eigenvalue problems for ODE (numerical methods)
34L16Numerical approximation of eigenvalues and of other parts of the spectrum
34A08Fractional differential equations
26A33Fractional derivatives and integrals (real functions)