Numerical solution of generalized time-fractional wave equation based on lattice Boltzmann method

Abstract This paper proposes an effective lattice Boltzmann method for the generalized time-fractional wave equation in the Caputo sense. The Caputo derivative term is firstly treated through numerical differentiation and the application of the composite integration rule. Subsequently, the generalized time-fractional wave equation is approximated to align with the standard form. By appropriately selecting auxiliary distribution functions, the macroscopic equation is properly recovered using the Chapman-Enskog expansion technique. A series of numerical comparisons show that the proposed method agrees well with the analytical solution, surpassing the accuracy of previous models. The efficiency of the proposed lattice Boltzmann model is thus validated.