This paper focuses on the numerical solution of the time-fractional telegraph equation in Caputo sense with 1 < β < 2. The time-fractional telegraph equation models neutron transport inside the core of a nuclear reactor. The proposed numerical solution consists of two stages. First, the time-discretized scheme of this equation is obtained by the Crank-Nicolson method. The stability and convergence of results from the semi-discretized scheme are presented. In the second stage, the numerical approximation of the unknown function at specific points is achieved through the collocation method using the moving least square method. The numerical experiments analyze the impact of some parameters of the proposed method.

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