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Least squares finite-element solution of a fractional order two-point boundary value problem. (English) Zbl 1069.65094
This paper deals with approximation of fractional differential equations on finite domains using variational methods. A least squares variational form for two point boundary value problems containing a fractional differential operator is derived and the existence and uniqueness results are proven. Error estimates for the variational form for piecewise linear trial elements are presented. Two numerical results are given.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
65L70Error bounds (numerical methods for ODE)