A new reproducing kernel method for solving the fractional differential equations

In this paper, we investigate the solution of fractional differential equations (FDEs) based on the reproducing kernel method. A reproducing kernel space is constructed using Legendre polynomials. Within this space, the ɛ -approximate method is applied to analyze the condition number of the matrix, and the stability and convergence of the proposed algorithm are examined. Finally, three numerical examples are presented to verify the effectiveness of the method. The obtained absolute errors are smaller than those reported in the reference literatures. This work provides an accurate and reliable numerical tool for solving FDEs.