The numerical solution for the time fractional advection‐diffusion problem in one‐dimension with the initial‐boundary condition is proposed in this paper by B‐spline finite volume element method. The fractional derivative is Caputo in the proposed scheme. The stability of the proposed numerical method is studied, and the numerical results presented support the theoretical results.

In this paper, the time-fractional advection-diffusion equation is solved by a cubic B-spline collocation method. For the fractional derivative we use the concept of the fractional derivative of Capato. Calculating of this numerical scheme is very simple. The presented numerical scheme is unconditional stable and highly accurate. We also obtain some error estimations with L2-norm and L[?]-norm.