Burgers' equation

Time derivative

Pure mathematics

Mathematics

Kernel (algebra)

Partial differential equation

Fractional calculus

Mathematical analysis

B-spline

Discretization

Applied mathematics

Results in Physics

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.

Numerical solutions of time fractional Burgers’ equation involving Atangana–Baleanu derivative via cubic B-spline functions