Analytical solutions of moving boundary problems for the time-fractional diffusion equation
Analysis of PDEs
2023-01-04 v2
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.
Keywords
Cite
@article{arxiv.2212.11794,
title = {Analytical solutions of moving boundary problems for the time-fractional diffusion equation},
author = {M. Rodrigo},
journal= {arXiv preprint arXiv:2212.11794},
year = {2023}
}