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Moreover, we prove that the resulting scheme can preserve the mass and energy conservation laws. Second, we show Crank-Nicolson scheme for two dimension fractional Klein-Gordon-Schr\u00f6dinger equations, and the proposed scheme preserves the mass and energy conservation laws in discrete formulations. However, the obtained discrete system is nonlinear system. Then, we show a equivalent form of fractional Klein-Gordon-Schr\u00f6dinger equations by introducing some new auxiliary variables. The new system is discretized by the high central difference scheme and scalar auxiliary variable scheme, and a linear discrete system is obtained, which can preserve the energy conservation law. Finally, the numerical experiments including one dimension and two dimension fractional Klein-Gordon-Schr\u00f6dinger systems are given to verify the correctness of theoretical results.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2023019","type":"journal-article","created":{"date-parts":[[2023,1,14]],"date-time":"2023-01-14T12:33:01Z","timestamp":1673699581000},"page":"463-493","source":"Crossref","is-referenced-by-count":0,"title":["Structure-preserving scheme for one dimension and two dimension fractional KGS equations"],"prefix":"10.3934","volume":"18","author":[{"given":"Junjie","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistical, Pu'er University, Yunnan, 665000, China"}]},{"given":"Yaping","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Science, Shaoyang University, Hunan, 422000, China"}]},{"given":"Liangliang","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Science, Xi'an Shiyou University, Shaanxi, 710065, China"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2023019-1","unstructured":"B. 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