The modified linearized difference scheme for parabolic fractional p -Laplace equations with bounded and globally Hölder continuous data

By combining the discretization scheme of the fractional p-Laplace operator with the modified Euler method, we develop a modified linearized difference scheme for solving the parabolic fractional p-Laplace equations. We analyse the existence and uniqueness, regularity, stability and convergence of the numerical solutions. In addition, some numerical experiments are performed to validate the effectiveness of the proposed algorithm. It is shown that, compared to the explicit method, our method has higher convergence accuracy.