Modified Atangana-Baleanu Caputo Operator for Time-Fractional Kuramoto-Sivashinsky Equation via Quintic B-Splines

Abstract

Abstract A novel numerical scheme for the time-fractional Kuramoto-Sivashinsky equation is presented in this article. A modification of the Atangana-Baleanu Caputo derivative known as the modified Atangana-Baleanu Caputo operator is introduced for the time-fractional derivative. A Taylor series-based formula is used to derive a second-order accurate approximation to the modified Atangana-Baleanu Caputo derivative. A linear combination of the quintic $B$-spline basis functions is used to approximate the functions in spatial direction. Moreover, through rigorous analysis, it has been proved that the present scheme is unconditionally stable and convergent. Finally, two test problems are solved numerically to demonstrate the proposed method's superconvergence and accuracy.