فهرست نشریات علمی دسترسی آزاد ایران

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.