Title: Application of Hat function for delay fractional optimal control problems

Authors: Amir Ahmad Khajehnasiri; Reza Ezzati; Mostafa Safavi; A. Jafari

Addresses: Department of Mathematics, Islamic Azad University, North Tehran Branch, Tehran, Iran ' Department of Mathematics, Islamic Azad University, Karaj Branch, Karaj, Iran ' Department of Mathematics, University of Texas at Dallas, Richardson, USA ' Department of Mathematics, Islamic Azad University, Khalkhal Branch, Khalkhal, Iran

Abstract: In this paper, we present a special class of fractional operational matrices to find the solution of the delay optimal control problems of fractional order. The solution is based on the Hat functions. Despite the complexity of the solution for delay systems, the most advantages of using Hat functions are the efficiency, reliability, and simplicity. To illustrate the proposed method, some numerical examples have been presented. Comparison with other methods and the numerical results show that the given numerical method is so accurate and effective to find the approximate solution of fractional delay systems as well as the delay fractional optimal control problems.

Keywords: delay; Hat functions; operational matrix; optimal control problems; block pulse function; BPF.

DOI: 10.1504/IJOR.2023.135504

International Journal of Operational Research, 2023 Vol.48 No.4, pp.494 - 508

Received: 15 Jul 2020
Accepted: 08 Mar 2021
Published online: 15 Dec 2023 *

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