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

2022/12/06 by M. Rodrigo, Rodrigo, M.
Mathematics · Engineering · #Fractional Differential Equations Solutions #Differential Equations and Numerical Methods #Brake Systems and Friction Analysis

paper · pdf · doi:10.48550/arxiv.2212.11794

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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