Cauchy problem for the Caputo-type time fractional Cahn–Hilliard equation in \({\mathbb {R}}^3\) is examined. The local existence and uniqueness of mild solutions and strong solutions are obtained for the initial data \(u_0\) satisfying \(u_0-{\bar{u}}\in L^\infty ({\mathbb {R}}^3)\cap L^1({\mathbb {R}}^3)\), where \({\bar{u}}\) is an equilibrium constant. The local solutions are extended globally if \(u_0-{\bar{u}}\) is small in \(L^1({\mathbb {R}}^3)\). These results are consistent with those of the traditional Cahn–Hilliard equation such as the property of mass conservation. However, extra difficulties arise in dealing with the singularity of Mittag-Leffler operators and non-Markovian property in the Caputo-type time fractional problem.

研究了\（{\ mathbb {R}} ^ 3 \）中Caputo型时间分数Cahn–Hilliard方程的柯西问题。在L ^ \ infty（{\ mathbb {R}} ^ 3中满足\（u_0-{\ bar {u}} \的初始数据\（u_0 \）获得温和解和强解的局部存在和唯一性）\ cap L ^ 1（{\ mathbb {R}} ^ 3）\），其中\（{\ bar {u}} \）是一个平衡常数。如果\（u_0-{\ bar {u}} \）在\（L ^ 1（{\ mathbb {R}} ^ 3）\）中较小，则全局扩展本地解决方案。这些结果与传统的Cahn-Hilliard方程（例如质量守恒性质）一致。但是，在Caputo型时间分数问题中，处理Mittag-Leffler算子的奇异性和非马尔可夫性质会产生额外的困难。