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Fractional truncated exponential method for linear fractional optimal control problems

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  • Ounamane, Said
  • Sadek, Lakhlifa
  • Abouzaid, Bouchra
  • Sadek, El Mostafa

Abstract

In this paper, we employ the Caputo fractional derivative (CFD) approach and utilize the truncated exponential method to tackle linear fractional optimal control problems (FOCPs) with equality and inequality constraints in multi-dimensional settings. By applying the truncated exponential method, we transform the FOCP into a system of algebraic equations that can be readily solved. Our analysis extends to the convergence and error estimation (EE) of truncated exponential method polynomials, and we introduce a residual correction procedure to refine error estimates. To assess the effectiveness and applicability of the proposed method, we conduct experiments on three different examples and compare our results with those of the previously obtained ones. Our findings yield very satisfactory results, and in some cases, we obtain exact solutions.

Suggested Citation

  • Ounamane, Said & Sadek, Lakhlifa & Abouzaid, Bouchra & Sadek, El Mostafa, 2025. "Fractional truncated exponential method for linear fractional optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 408-426.
    • Handle: RePEc:eee:matcom:v:232:y:2025:i:c:p:408-426
    DOI: 10.1016/j.matcom.2025.01.009
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    References listed on IDEAS

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    1. Marzban, Hamid Reza, 2022. "A generalization of Müntz-Legendre polynomials and its implementation in optimal control of nonlinear fractional delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Ahmad, Wajdi M. & El-Khazali, Reyad, 2007. "Fractional-order dynamical models of love," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1367-1375.
    3. Sadek, Lakhlifa & Bataineh, Ahmad Sami & Isik, Osman Rasit & Alaoui, Hamad Talibi & Hashim, Ishak, 2023. "A numerical approach based on Bernstein collocation method: Application to differential Lyapunov and Sylvester matrix equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 475-488.
    4. Yüzbaşı, Şuayip & Yıldırım, Gamze, 2022. "A collocation method to solve the parabolic-type partial integro-differential equations via Pell–Lucas polynomials," Applied Mathematics and Computation, Elsevier, vol. 421(C).
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