A Research Note on a Solution of Stefan Problem with Fractional Time and Space Derivatives

Abstract

Stefan problem based on nonlocal heat conduction equation with fractional-time derivatives has been solved. The approach suggests a generalized time-dependent Stefan boundary condition defined by expression ϑ(α, β, τ) = σ(α, β)τ^(α/β). The solution developed shows that the phase change boundary co-ordinate ϑ depends on time τ and the parameters α (0<α≤1) and β (1<β≤2) which are the fractional orders with respect to the time and the space co-ordinate , respectively. A practical example with ice-water system was used to exemplify the solution with both α and β near to α = 1 and β = 1 (the classical problem).