Existence and uniqueness of the global smooth solution for the generalized nonautonomous fractional long-short wave equations with initial and periodic boundary conditions is proved by using uniform priori esti-mates and Galerkin method.%运用一致先验估计和Galerkin方法，研究了广义非自治分数阶长短波方程的周期初边值问题光滑解的整体存在性和唯一性。
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