SPECTRAL METHODS COMBINED WITH OPERATIONAL MATRICES FOR FRACTIONAL OPTIMAL CONTROL PROBLEMS: A REVIEW

Ashpazzadeh E., Lakestanı M., Fatholahzadeh A.

Applied and Computational Mathematics, cilt.20, sa.2, ss.209-235, 2021 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 2
  • Basım Tarihi: 2021
  • Dergi Adı: Applied and Computational Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.209-235
  • Anahtar Kelimeler: Caputo Fractional Derivative, Fractional Optimal Control Problems, Operational Matrices, Riemann-Liouville Fractional Integral
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

The object of this article is to present some spectral methods that have been developed over the years for solving a class of fractional optimal control problems. Recently, operational matrices of fractional derivatives and integrals for various bases were adapted for solving these types of problems. By using operational matrices in conjunction with the spectral schemes, a fractional optimal control problem converts to an optimization problem, which produce highly accurate solutions for such problems. Moreover, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Bernoulli, fractional order Chebyshev, Genocchi, Boubaker and Bernstein polynomials, and for some wavelet and scaling functions such as, linear B-spline scaling function and biorthogonal multiwavelets, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. Several examples are presented to illustrate the numerical and theoretical properties of the reviewed methods.