<p>This paper develops an efficient and accurate computational technique based on an extended cubic B-spline (ExCBS) collocation method for time-fractional convection–diffusion equations with variable coefficients. The time-fractional derivative is defined in the Caputo sense, enabling realistic modelling of memory and hereditary effects in complex transport phenomena. Spatial discretization exploits the smoothness of the ExCBS basis functions, while a finite-difference scheme is employed for temporal discretization. A von Neumann analysis demonstrates that the method is unconditionally stable for the constant-coefficient case, and a rigorous error analysis confirms second-order convergence in time. These theoretical results are verified numerically through temporal empirical-order-of-convergence tests on both homogeneous and heterogeneous, advection-dominated examples. Comprehensive numerical experiments show that the proposed method achieves higher accuracy with reduced computational cost compared with existing approaches, such as Chebyshev collocation and local discontinuous Galerkin finite element methods. In addition, a parameter sensitivity study indicates that appropriate tuning of the free spline parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> further enhances accuracy and suppresses oscillations. The robustness of the method is illustrated using a representative transport problem, highlighting its practical applicability in engineering and applied sciences. Overall, this work extends B-spline-based techniques to a broader class of fractional models and provides a reliable and generalizable computational tool for memory-dependent transport processes in heterogeneous media.</p>