Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method

Mohammad Maleki ^[1] ; Ishak Hashim ^[1] ; Saeid Abbasbandy ^[2] ; A. Alsaedi ^[3]
1. [1] National University of Malaysia
  
  National University of Malaysia
  
  Malasia
2. [2] Imam Khomeini International University
  
  Imam Khomeini International University
  
  Irán
3. [3] King Abdulaziz University
  
  King Abdulaziz University
  
  Arabia Saudí
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Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 283, Nº 1 (1 August 2015), 2015, págs. 41-57
Idioma: inglés
DOI: 10.1016/j.cam.2015.01.019
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Resumen
- 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.