This article deals with designing and analyzing a higher order stable numerical analysis for the time‐fractional Kuramoto–Sivashinsky (K‐S) equation, which is a fourth‐order non‐linear equation. The fractional derivative of order
present in the considered problem is taken into Caputo sense and approximated using the
scheme. In space direction, the discretization process uses quintic
‐spline functions to approximate the derivatives and the solution of the problem. The present approach is unconditionally stable and is convergent with rate of accuracy
, where
and
denote the space and time step sizes, respectively. We have also noted that the linearized version of the K‐S equation leads the rate of accuracy to
. The present approach is also highly effective for the time‐fractional Burgers' equation. We have shown that the present approach provides better accuracy than the
scheme with the same computational cost for several linear/non‐linear problems, with classical as well as fractional time derivatives.