论文标题
时间分数扩散方程的移动边界问题的分析解决方案
Analytical solutions of moving boundary problems for the time-fractional diffusion equation
论文作者
论文摘要
考虑时间衍生物是Caputo或Riemann-Liouville型的，考虑时间折叠扩散方程。使用嵌入方法得出了在有限和无界域上与时间相关边界条件的一般初始有限值问题的解决方案。用两参数辅助函数表示的初始有限值问题的解决方案用于获得移动边界问题的分析解决方案。特别是，发现了诺伊曼解决方案对经典Stefan问题的“分数”类似物，以融化冰。
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and unbounded domains is derived using the embedding method. The solution of the initial-boundary value problem, expressed in terms of a two-parameter auxiliary function, is used to obtain analytical solutions of moving boundary problems. In particular, a 'fractional' analogue of the Neumann solution to a classical Stefan problem for melting ice is found.
