Spectral Collocation Approach with Shifted Chebyshev Third-Kind Series Approximation for Nonlinear Generalized Fractional Riccati Equation

This study presents a new efficient collocation approach to handle the nonlinear generalized fractional Riccati equation. The linearization formula of the product of two shifted Chebyshev polynomials of the third kind (SCP3K) is used to deal with the quadratic term, resulting in a system of nonlinear algebraic equations. Then Newton’s iterative method is used to solve this system and obtain the approximate solution. Also, numerical comparisons between the presented procedure with different numerical methods in the current literature are held. The numerical outcomes confirm that the proposed procedure is precise, computationally efficient, and easy to implement.