Abstract
The current paper uses the cubic B-spline functions and θ-weighted scheme to achieve numerical solutions of the time fractional Burgers’ equation with Atangana–Baleanu derivative. A non-singular kernel is involved in the Atangana–Baleanu fractional derivative. For discretization along temporal and spatial grids, the proposed numerical technique employs the finite difference approach and cubic B-spline functions, respectively. This scheme is unconditionally stable and second order convergent in spatial and temporal directions. The presented approach is endorsed by some numerical examples, which show that it is applicable and accurate.
•An efficient numerical technique based on CBS is developed for the TFBE Involving ABFD.•Fourier stability and convergence of the suggested model are proved.•Order of convergence theoretically and numerically is found.•Four examples have shown to check the feasibility and validity of the technique.•The scheme is novel and as far as we are aware, it has never been employed for this purpose before.