This paper investigates the conservation of mass and energy in the space-fractional Klein-Gordon-Schrödinger system with fractional Laplacian operators. Firstly, the invariant energy quadratization method is applied to transform the original system into an equivalent form. For spatial discretization, Fourier spectral methods are employed, yielding a semi-discrete scheme. Subsequently, an invariant energy quadratization Runge-Kutta approach is used for temporal discretization, resulting in a fully discrete scheme. Owing to its diagonally implicit structure, the proposed scheme is both highly accurate and efficient while preserving mass and energy exactly. Numerical experiments are conducted to verify the accuracy and conservation properties of the method.
Jiang et al. (Sun,) studied this question.