Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

Numerical method for solving a class of two-dimensional fractional optimal control problem of via operational matrices of Legendre polynomial

Document Type : Original Paper

Authors
yaser nouralizade
Mahmoud Behroozifar
Mohsen Alipour
Department of Mathematics, Babol Noshirvani university of tecgnology, Babol, Iran
10.22055/jamm.2020.24146.1516
Abstract
‎ ‎In ‎‎t‎his article, we present a ‎‎‎numerical ‎method ‎for‎ solving a class of ‎two-‎dimensional fractional optimal control problems ‎by‎ the Legendre ‎polynomial‎ basis with fractional operational ‎matrix‎. It should be mentioned that the dynamic system of the problem is based on the Caputo fractional partial derivative. This method, the dual integral is approximated by ‎Gauss-‎Legendre rule, and then by using the Lagrangian equation, a nonlinear equation is obtained. This nonlinear equation set is solved by Newton's iterative method and unknown coefficients is determined. Finally, the proposed method was applied on a fractional problem with the different degree of fractional derivative. Also, the CPU time of method is exhibited. It is notable that all calculations were obtained by the Mathematica software.
Keywords
Partial differential of fractional Caputo
Legendre polynomial
Operational matrices
Legendre-Gauss integration rule
Subjects
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Applications of Fractional Differential Equations, Elsevier, San Diego.
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solving fractional Riccati differential equations, Applied Mathematics
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 Momani, S. and Noor, M.A. (2006). Numerical methods for fourth-order
fractional integro-differential equations, Applied Mathematics and
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Gejji, V.D. and Jafari, H. (2007). Solving a multi-order fractional
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548
Journal of Advanced Mathematical Modeling
Volume 10, Issue 1
May 2020
Pages 1-18

  • Receive Date 19 November 2017
  • Revise Date 11 October 2019
  • Accept Date 17 January 2020