A SPACE-FRACTIONAL STEFAN PROBLEM FOR ADVECTION-DISPERSION: ANALYTICAL AND COMPUTATIONAL APPROACHES

Abstract

 This article presents an investigation of the space-fractional Stefan problem, a mathematical model formulated to describe phase
transition phenomena in materials where heat transfer exhibits anoma-lous diffusion governed by spatial fractional derivatives of the Caputo
type. The proposed formulation effectively captures nonlocal interactions and memory effects commonly observed in media with complex
thermal properties, features that classical differential equations fail to accurately represent. The fractional Stefan problem finds broad applica-
bility in modeling heat conduction in heterogeneous materials, solidification of alloys, cryopreservation of biological tissues, moisture transport
in porous structures, and thermal evolution in geological formations. To facilitate the analysis, a similarity transformation is employed to re-
duce the governing space-fractional partial differential equation (PDE) to an equivalent fractional ordinary differential equation (ODE), pre-
serving the essential characteristics of the anomalous diffusion process. The resulting fractional ODE is then solved using the Laplace Adomian
Decomposition Method (LADM), which provides an efficient analytical approach for obtaining a series solution while satisfying the imposed initial and boundary conditions. The solution is expressed in terms of the three-parameter Mittag-Leffler function, thereby reflecting the inherent
nonlocality of fractional diffusion. Furthermore, the derived solutions are shown to converge to their classical counterparts in the appropriate
limiting cases, confirming the validity of the proposed approach. Numerical results are presented to verify the effectiveness and applicability
of the proposed method