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Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method. (English) Zbl 1311.65087
Summary: This paper presents an adaptive Legendre-Gauss pseudospectral method for solving a type of constrained fractional variational problems (FVPs). The fractional derivative is defined in the Caputo sense. In the presented method, by dividing the domain of the problem into a uniform mesh the given FVP reduces to a nonlinear mathematical programming problem, and there is no need to solve the complicated fractional Euler-Lagrange equations. The method developed in this paper adjusts both the mesh spacing and the number of collocation points on each subinterval in order to improve the accuracy. The method is easy to implement and yields very accurate results. Some error estimates and convergence properties of the method are discussed. Numerical examples are included to confirm the efficiency and convergence of the proposed method.

MSC:
65K10 Numerical optimization and variational techniques
49J15 Existence theories for optimal control problems involving ordinary differential equations
49M37 Numerical methods based on nonlinear programming
Software:
Matlab
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