10.57647/mathsci.89bj.w891

A Robust Galerkin Fractional Taylor Technique to Solve Multi-Dimensional Fractional Optimal Control Problems with Inequality Constraints

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  • Lakhlifa Sadek1,2,
  • Ibtisam Aldawish3,
  • Zakia Hammouch4,5,
  • Ahmad Shafee6,
  • Ioan-Lucian Popa7,8,
  1. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, Tamilnadu, India
  2. Department of Mathematics, Faculty of Sciences and Technology, Al-Hoceima, Abdelmalek Essaadi University, Tetouan, Morocco
  3. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
  4. Department of Medical Research, China Medical University Hospital, Taichung, Taiwan
  5. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-Ro, Dongdaemun-Gu, Seoul, 02447, South Korea
  6. Laboratory Technology Department , College of Technological Studies, Public Authority for Applied Education and Training (PAAET), Shuwaikh, Kuwait
  7. Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, 510009, Alba Iulia, Romania
  8. Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091, Brasov, Romania

Received: 2025-11-20

Revised: 2026-04-24

Accepted: 2026-05-14

Published in Issue 2026-06-03

Copyright (c) 2026 Lakhlifa Sadek, Ibtisam Aldawish, Zakia Hammouch, Ahmad Shafee, Ioan-Lucian Popa (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Sadek, L., Aldawish, I., Hammouch, Z., Shafee, A., & Popa, I.-L. (2026). A Robust Galerkin Fractional Taylor Technique to Solve Multi-Dimensional Fractional Optimal Control Problems with Inequality Constraints. Mathematical Sciences. https://doi.org/10.57647/mathsci.89bj.w891
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Abstract

A new computational approach is presented for solving MFOCPs subject to Caputo fractional dynamics by means of Galerkin projection technique along with fractional Taylor polynomial expansions. The method successfully deals with constraints in the form of both equalities and inequalities.  An important feature of the new method includes deriving an operational matrix based on fractional Taylor polynomials such that, using the Galerkin approach, the problem under study is reduced to a set of algebraic equations. Convergence analysis of the Taylor series expansions is investigated in detail. The performance of the approach is confirmed by applying it to four problems in comparison with other existing approaches in the literature.

MSC 2010: 49M05; 65T60

Keywords

  • MFOCPs,
  • Caputo fractional derivative (CFD),
  • Riemann-Liouville fractional integral (RLI),
  • Fractional Taylor polynomials,
  • Galerkin method,
  • Error estimation
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