Solving Fractional Optimal Control Problems Involving Caputo–Fabrizio Derivative Using Hermite Spline Functions

Noori Dalawi A., Lakestanı M., Ashpazzadeh E.

Iranian Journal of Science, cilt.47, sa.2, ss.545-566, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s40995-022-01404-4
  • Dergi Adı: Iranian Journal of Science
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.545-566
  • Anahtar Kelimeler: Caputo-Fabrizio derivative, Collocation method, Fractional optimal control, Hermite spline functions, Operational matrix of fractional derivative
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In the current research, we develop a collocation method based on the biorthogonal Hermite cubic spline functions to solve a class of fractional optimal control problems using Caputo–Fabrizio derivative operator. We design dual bases for Hermite cubic spline functions for the first time in this work. So, we present two direct and efficient algorithms to solve a class of fractional optimal control problems. Two new operational matrices of Caputo–Fabrizio fractional derivative are derived using Hermite cubic spline functions. By employing these matrices, we reduce these problems to systems of algebraic equations. Illustrative examples are examined to demonstrate the important features of the new algorithm.