Generalized Jacobi Wavelet Solutions of Fractional Nonlinear Differential Equations

Abstract In this study, generalized Jacobi wavelets are introduced for fractional nonlinear differential equations, and an approximate solution method based on these wavelets is proposed. Generalized Jacobi wavelets, which are an extended form of classical Jacobi polynomials, offer an effective approach for solving fractional-order differential equations due to their orthogonality and high convergence properties. The proposed method is applied to obtain approximate solutions of fractional Riccati differential equations, which hold a significant place within the class of fractional nonlinear differential equations. The efficiency and accuracy of the method are demonstrated through various numerical examples. The results show that the proposed approach achieves higher accuracy and faster convergence compared to traditional methods.