Two equivalent Stefan's problems for the time fractional diffusion equation

Sabrina Roscani, Eduardo Marcus
2013 Fractional Calculus and Applied Analysis  
AbstractTwo Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order α ∈ (0, 1) is taken in the Caputo sense. The first one has a constant condition on x = 0 and the second presents a flux condition T x(0,t) = q/t α/2. An equivalence between these problems is proved and the convergence to the classical solutions is analyzed when α ↗ 1 recovering the heat equation with its respective Stefan's condition.
doi:10.2478/s13540-013-0050-7 fatcat:y3rin4lapnhunngs5t33dwraui