Efficient Spectral Collocation Schemes for Nonlinear ψ-Caputo Fractional Riccati Differential Equations with Variable-Order

Abstract

This article presents a spectral method for estimating solutions of the nonlinear Variable-Order Caputo ψ-Fractional Riccati Differential Equation (VOC-ψ-FRDE). First, the solution and its ψ-fractional derivatives are expressed using a series of Shifted Legendre Polynomials (SLPs). Then, the expansion coefficients are determined by transforming the VOC-ψ-FRDE along with its associated conditions into an algebraic system. The effectiveness and feasibility of the proposed approach are demonstrated through various numerical tests.