A second order Crank-Nicolson scheme for fractional Cattaneo 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 Crank-Nicolson finite difference scheme to solve fractional Cattaneo equation based on the new fractional derivative is introduced and analyzed. Some a priori estimates of discrete L∞(L2) errors with optimal order of convergence rate O(τ2+h2) are established on uniform partition. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.