Numerical Approach of Cattaneo Equation with Time Caputo-Fabrizio Fractional Derivative

In the paper, we consider a type of Cattaneo equation with time fractional derivative without singular kernel based on fourth-order compact finite difference (CFD) in the space directions. In case of two dimensional, two alternating direction implicit (ADI) methods are proposed to split the equation into two separate one dimensional equations. The time fractional derivation is described in the Caputo-Fabrizio’s sense with scheme of order O(τ2). The solvability, unconditional stability and H1 norm convergence of the scheme are proved. Numerical results confirm the theoretical results and the effectiveness of the proposed scheme.