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Al-Hakeem, Muhammed Hassanein, Mahmoudi, Mahmoud, Ahmed Al-Jilawi, Ahmed Sabah. (1405). A Hybrid Orthogonal Polynomial Approach for Optimal Control of Fractional Parabolic PDEs: Combining Legendre, Chebyshev, and Jacobi Polynomials. فصلنامه علمی زیست فناوری گیاهان زراعی, 11(2), 153-177. doi: 10.30473/coam.2026.76804.1378
Muhammed Hassanein Al-Hakeem; Mahmoud Mahmoudi; Ahmed Sabah Ahmed Al-Jilawi. "A Hybrid Orthogonal Polynomial Approach for Optimal Control of Fractional Parabolic PDEs: Combining Legendre, Chebyshev, and Jacobi Polynomials". فصلنامه علمی زیست فناوری گیاهان زراعی, 11, 2, 1405, 153-177. doi: 10.30473/coam.2026.76804.1378
Al-Hakeem, Muhammed Hassanein, Mahmoudi, Mahmoud, Ahmed Al-Jilawi, Ahmed Sabah. (1405). 'A Hybrid Orthogonal Polynomial Approach for Optimal Control of Fractional Parabolic PDEs: Combining Legendre, Chebyshev, and Jacobi Polynomials', فصلنامه علمی زیست فناوری گیاهان زراعی, 11(2), pp. 153-177. doi: 10.30473/coam.2026.76804.1378
Al-Hakeem, Muhammed Hassanein, Mahmoudi, Mahmoud, Ahmed Al-Jilawi, Ahmed Sabah. A Hybrid Orthogonal Polynomial Approach for Optimal Control of Fractional Parabolic PDEs: Combining Legendre, Chebyshev, and Jacobi Polynomials. فصلنامه علمی زیست فناوری گیاهان زراعی, 1405; 11(2): 153-177. doi: 10.30473/coam.2026.76804.1378

A Hybrid Orthogonal Polynomial Approach for Optimal Control of Fractional Parabolic PDEs: Combining Legendre, Chebyshev, and Jacobi Polynomials

Control and Optimization in Applied Mathematics
مقاله 8، دوره 11، شماره 2 - شماره پیاپی 22، مرداد 2026، صفحه 153-177
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.30473/coam.2026.76804.1378
نویسندگان
Muhammed Hassanein Al-Hakeem* 1؛ Mahmoud Mahmoudi1؛ Ahmed Sabah Ahmed Al-Jilawi2
1Department of Mathematics, College of Science‎, ‎University of Qom‎, ‎Qom‎, ‎Iran
2Department of Mathematics, Faculty of Education, College For Pure Sciences Babylon, University Babylon, Iraq
چکیده
This paper presents a novel hybrid orthogonal polynomial method for solving optimal control problems governed by fractional parabolic PDEs. By strategically weighting and combining these polynomial bases, the method adaptively leverages their respective strengths to achieve superior approximation properties. The proposed approach combines the spectral accuracy of Legendre polynomials, the minimax properties of Chebyshev polynomials, and the flexibility of Jacobi polynomials to create a robust numerical framework. The hybrid orthogonal polynomial method is applied to discretize the fractional parabolic PDEs, and an efficient numerical scheme is developed to solve the resulting optimal control problem. Numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed approach, showing significant improvements over traditional radial basis function methods. The results highlight the potential of the hybrid orthogonal polynomial method for solving complex optimal control problems in science and engineering.

تازه های تحقیق
  • Fractional parabolic optimal control problems pose substantial computational challenges due to the intrinsic nonlocal memory effects of fractional derivatives and the tight coupling between state and control variables.
  • A novel hybrid orthogonal polynomial framework is proposed, systematically integrating Legendre, Chebyshev, and Jacobi polynomials to simultaneously exploit spectral accuracy, minimax optimality, and parametric flexibility.
  • The hybridization strategy yields a stable and highly accurate spectral scheme, capable of adaptively capturing complex spatial–temporal solution behaviors while maintaining well-conditioned algebraic systems.
  • The resulting numerical method demonstrates clear superiority over classical radial basis function approaches, delivering lower error norms, faster convergence, and enhanced computational efficiency for fractional optimal control problems in science and engineering.
کلیدواژه‌ها
Meshless method؛ Fractional parabolic PDE؛ Orthogonal polynomials؛ Spectral methods؛ Optimal control
مراجع

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