This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity of fractional derivatives, we convert the original partial differential equations into a coupled ordinary differential system. Through Laplace transform and maximum principle arguments, we reveal a dichotomy in decay behavior: When the highest fractional order is less than one, solutions exhibit sublinear decay, whereas systems with the highest order equal to one demonstrate a distinct superlinear decay pattern. This phenomenon fundamentally distinguishes coupled systems from single fractional diffusion equations, where such accelerated superlinear decay never occurs. Numerical experiments employing finite difference methods and implicit discretization schemes validate the theoretical findings.

翻译：本文研究了具有时空变化耦合系数的弱耦合时间分数阶亚扩散方程组的初边值问题。通过结合能量方法与分数阶导数的强制性，我们将原始偏微分方程组转化为耦合常微分方程组。借助拉普拉斯变换与最大值原理论证，我们揭示了衰减行为的二分现象：当最高分数阶小于1时，解呈现亚线性衰减；而当最高阶等于1时，系统展现出显著不同的超线性衰减模式。这一现象从根本上将耦合系统与单一分数阶扩散方程区分开来——在后者中，此类加速的超线性衰减永远不会出现。采用有限差分法与隐式离散格式的数值实验验证了理论结果。