Two equivalent Stefan's problems for the Time Fractional Diffusion Equation

Original · EN

Two Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order ∈ (0,1) is taken in the Caputo's sense. The first one has a constant condition on x = 0 and the second presents a flux condition Tₓ (0, t) = q t /2. An equivalence between these problems is proved and the convergence to the classical solutions is analysed when 1 recovering the heat equation with its respective Stefan's condition.