Fast shifted Legendre wavelets method for solving two-dimensional nonlinear fractional partial differential equations

Abstract The primary objective of this paper is to develop an efficient numerical method for solving two-dimensional nonlinear fractional partial differential equations in both temporal and spatial domains. The proposed approach combines a fast algorithm with Shifted Legendre wavelets to efficiently handle fractional derivatives in space and time. The resulting scheme is straightforward to implement and computationally efficient. An interpolation technique is employed to convert the nonlinear problems into equivalent linear forms, after which the proposed method is applied. Convergence analysis confirms that the numerical solutions are in good agreement with the corresponding analytical solutions. Numerical results, presented in both tabular and graphical formats, further demonstrate the accuracy and efficiency of the proposed method. In addition, comparisons with existing methods from the literature are provided to highlight the superior performance of the proposed approach.