Qualitative and Numerical Analysis to a Time-Fractional Stefan Convection-Diffusive Model Using Riemann-Liouville and Caputo Operators

This paper introduces a model of the fractional Stefan Problem(SP) to linear convection and diffusion forces.We assess the memory effect in the studied model.Rescaling technique is used to reduce the fractional PDEs under some restrictions.The fractional derivative method, particularly Riemann-Liouville and Caputo derivatives, is used to derive the given model.The self-similar solutions and the interface function are estimated to the time fractional SP model including boundary and Stefan conditions.In addition, we estimate an approximated numerical solution the time-fractional convection-diffusion equation by applying the Sumudu decomposition method (SDM).The proposed method depends on applying the Sumudu transform of the Caputo fractional derivative operator and then using the fractional integral of Riemann-Liouville.Furthermore, a special solution to this model is valid and applicable.