A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative

Recently, Caputo and Fabrizio introduce a new derivative with fractional order which has the ability to describe the material heterogeneities and the fluctuations of different scales. In this article, a finite difference scheme to solve a quasilinear fractal mobile/immobile transport model based on the new fractional derivative is introduced and analysed. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. Some a priori estimates of discrete are established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.