An Extended Cubic B-Spline Galerkin Finite Element Method for Multi-Term Time-Fractional Differential Equations

This study presents an extended cubic B-spline Galerkin scheme for the numerical solution of multi-term time-fractional differential equations. The proposed formulation employs extended cubic B-splines together with the Caputo fractional derivative to model the time-fractional operators. Gauss quadrature is used to accurately evaluate the resulting integral. A stability analysis of the scheme is provided and its accuracy is assessed through L2 and L∞ error norms over different spatial nodes and mesh refinements. The numerical results demonstrate excellent agreement with the exact solutions, as illustrated in the tables and figures. These findings confirm the robustness, efficiency and reliability of the proposed method for solving multi-term time-fractional differential equations.