Analytical solutions of moving boundary problems for the time-fractional diffusion equation

M. Rodrigo

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arXiv · 2212.11794

Analytical solutions of moving boundary problems for the time-fractional diffusion equation

M. Rodrigo

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Abstract

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.

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M. Rodrigo. 2022-12-06. Analytical solutions of moving boundary problems for the time-fractional diffusion equation. https://arxiv.org/abs/2212.11794

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