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Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 158–182 | Cite as

Approximation methods for solving fractional optimal control problems

  • Samaneh Soradi Zeid
  • Sohrab EffatiEmail author
  • Ali Vahidian Kamyad
Article

Abstract

In this review paper, approximation methods for the free final time of fractional optimal control problems (FOCPs) are displayed. The considered problems mainly include the fractional differential equations (FDEs) with fractional derivatives (FDs). In this way, the considered tools and techniques mainly include the necessary optimal conditions in the form of two-point boundary value (TPBV) problem of fractional order. The Legendre operational, Ritz method and the Jacobi, Bernoulli and Legendre polynomials are extended as numerical methods for FOCPs accordingly. At the same time, the techniques for improving the accuracy and computation and storage are also introduced.

Keywords

Fractional optimal control problem Fractional differential equation Fractional derivative Fractional two-point boundary value problem Numerical approximation 

Mathematics Subject Classification

49M05 49M25 65K99 

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  • Samaneh Soradi Zeid
    • 1
  • Sohrab Effati
    • 1
    Email author
  • Ali Vahidian Kamyad
    • 1
  1. 1.Department of Applied Mathematics, Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

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