A computationally efficient method for a class of fractional variational and optimal control problems using fractional gegenbauer functions

Ahmed Zaki Mahamed Amin A. Z. M. A.

Romanian Reports in Physics, cilt.70, sa.109, ss.90-109, 2018 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70 Sayı: 109
  • Basım Tarihi: 2018
  • Dergi Adı: Romanian Reports in Physics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.90-109
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.