en عمومى General پژوهشي Research paper 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. Caputo-Fabrizio fractional derivative, Compact finite difference, Cattaneo equation, Alternating direction implicit method. 127 153 http://ijmsi.ir/browse.php?a_code=A-10-5488-1&slc_lang=en&sid=1 Zoleikha Soori zsoori@mail.kntu.ac.ir 100319475328460010868 100319475328460010868 Yes Department of Mathematics, K. N. Toosi University of Technology, P. O. Box: 1676-53381, Tehran, Iran Azim Aminataei ataei@kntu.ac.ir 100319475328460010869 100319475328460010869 No Department of Mathematics, K. N. Toosi University of Technology, P. O. Box: 1676-53381, Tehran, Iran