University of Tabriz Computational Methods for Differential Equations 2345-3982 Articles in Press 2025 09 13 A Spectral Tau Method Based on Lucas Polynomial Approximation for Solving the Nonlinear Fractional Riccati Equation 20344 10.22034/cmde.2025.67681.3237 EN Youssri Hassan Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt. Ahmed Gamal Atta Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt. Journal Article 2025 06 03 The nonlinear fractional Riccati equation (NFRE) can be solved using a unique spectral tau approach in this study that uses Lucas polynomials as basis functions. The fractional Caputo derivative and nonlinear terms can be handled effectively by explicit operational formulations when the Lucas basis is used. A tau projection is used to convert the problem into a nonlinear algebraic system, which is then solved by Gaussian elimination. The correctness and quick convergence of the suggested method are shown by a number of numerical tests that are backed by error analysis. https://cmde.tabrizu.ac.ir/article_20344_b03e462133db268053dd943cbf225135.pdf