中文摘要：

利用局部分数阶Taylor公式,导出了分数阶光滑函数等距节点三次Lagrange插值公式余项的精确估计式,并通过数值算例验证了理论分析的正确性，

英文摘要：

The sharp remainder estimation of cubic Lagrange interpolation with equidistant nodes is derived for fractional smooth functions based on local fractional Taylor＇s formula. Numerical examples verify the correctness of the theoretical analysis.