An improved numerical simulation for anomalous transport phenomena with redefined extended cubic B-spline functions

• A RECBS-based collocation scheme is developed for the TFGDE. • Caputo time-fractional derivative is discretized via a finite-difference method. • A shape parameter enhances flexibility over classical cubic B-splines. • Stability and convergence of the proposed scheme are rigorously analyzed. • Numerical results show improved accuracy compared with existing methods. • Excellent agreement is observed between numerical and exact solutions. This study presents a numerical framework based on redefined extended cubic B-spline (RECBS) functions for the solution of the time-fractional gas dynamics equation (TFGDE), which arises in the modeling of nonlinear wave propagation and interaction phenomena. The proposed methodology integrates a finite-difference scheme to discretize the Caputo time-fractional derivative, while RECBS functions are employed to approximate the solution in the spatial domain. The use of RECBS basis functions introduces additional flexibility through a shape parameter, allowing improved control over the solution profile compared to conventional spline-based approaches. A rigorous stability analysis is performed to ensure that computational errors remain bounded throughout the simulation. Additionally, a convergence analysis is conducted to measure the accuracy of the solution. The performance of the method is assessed through four test problems. Comparative numerical experiments show that the proposed approach produces smaller error norms than existing techniques. Graphical comparisons further confirm the excellent agreement between numerical and exact solutions. These results indicate that the proposed RECBS-based collocation method provides a flexible, accurate and reliable framework for solving nonlinear fractional differential equations.