In this work, we consider a fractional extension of the classical nonlinear wave equation, subjected to initial conditions and homogeneous Dirichlet boundary data. We consider space-fractional derivatives of the Riesz type in a bounded real interval. It is known that the problem has an associated energy which is preserved through time. The mathematical model is presented equivalently using the scalar auxiliary variable (SAV) technique, and the expression of the energy is obtained using the new scalar variable. The new differential system is discretized then following the SAV approach. The proposed scheme is a nonlinear implicit method which has an associated discrete energy, and we prove that the discrete model is also conservative. The present work is the first report in which the SAV method is used to design nonlinear conservative numerical method to solve a Hamiltonian space-fractional wave equations.

在这项工作中，我们考虑了初始条件和齐次Dirichlet边界数据的经典非线性波动方程的分数扩展。我们考虑有界实数区间中Riesz类型的空间分数导数。众所周知，问题具有随时间而保留的相关能量。使用标量辅助变量（SAV）技术等效地表示数学模型，并使用新的标量变量获得能量的表达式。然后采用SAV方法离散化新的差分系统。所提出的方案是一种具有关联离散能量的非线性隐式方法，我们证明了离散模型也是保守的。