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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:

65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
65L70 Error bounds for numerical methods for ordinary differential equations
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