Lattice Boltzmann Model for a Class of Time Fractional Partial Differential Equation

Abstract

This paper is concerned with the lattice Boltzmann (LB) method for a class of time fractional partial differential equations (FPDEs) in the Caputo sense. By utilizing the properties of the Caputo derivative and discretization in time, FPDEs can be approximately transformed into standard partial differential equations with integer orders. Through incorporating an auxiliary distribution function into the evolution equation, which assists in recovering the macroscopic quantity u, the LB model with spatial second-order accuracy is constructed. The numerical experiments verify that the numerical results are in good agreement with analytical solutions and that the accuracy of the present model is better than the previous solutions.