Abstract
The lattice Boltzmann method (LBM) was applied to numerically solve Riemann-Liouville spatial fractional-order telegraph equations. Firstly, the integral term of the fractional-order operator was discretized and the order of convergence was analyzed. Then, a 1D and 3-velocity (D1Q3) LBM evolution model with modified functions was established. The expressions of equilibrium distribution functions and correction functions were deduced by means of the Chapman-Enskog multi-scale analysis and the Taylor expansion technique. Therefore, the macroscopic equation was exactly recovered from the established evolution model. Numerical results show the stability and effectiveness of the model.
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