High-order difference scheme for the solution of linear time fractional Klein-Gordon equation

In this article, we apply a high-order difference scheme for the solution of time fractional Klein-Gordon equation. The time fractional derivative which has been described in the Caputo sense is approximated by a scheme of order $O(\tau^{3-\alpha}) 1 \alpha 2)$, and the space derivative is discretized with a sixth-order compact procedure. Numerical example shows the effectiveness and the spatial higher-order accuracy of the proposed scheme