We consider a family of initial boundary value problems governed by a fractional diffusion equation with Caputo derivative in time, where the parameter is the Newton heat transfer coefficient linked to the Robin condition on the boundary. For each problem we prove existence and uniqueness of solution by a Fourier approach. This will enable us to also prove the convergence of the family of solutions to the solution of the limit problem, which is obtained by replacing the Robin boundary condition with a Dirichlet boundary condition.

中文翻译：

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关于robin型分数扩散方程族初边值问题的收敛性

我们考虑一系列初始边值问题，这些问题由分数扩散方程和 Caputo 时间导数控制，其中参数是与边界上的 Robin 条件相关的牛顿传热系数。对于每个问题，我们通过傅里叶方法证明解决方案的存在性和唯一性。这也将使我们能够证明极限问题的解族的解的收敛性，这是通过将 Robin 边界条件替换为 Dirichlet 边界条件而获得的。