High‐order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo–Fabrizio fractional derivative

In this article, a local discontinuous Galerkin (LDG) method is studied for numerically solving the fractal mobile/immobile transport equation with a new time Caputo–Fabrizio fractional derivative. The stability of the LDG scheme is proven, and a priori error estimates with the second‐order temporal convergence rate and the (k + 1) th order spatial convergence rate are derived in detail. Finally, numerical experiments based on P^k, k = 0, 1, 2, 3, elements are provided to verify our theoretical results.