Behavior of Space-Fractional Stefan Problems Under Convection Diffusion Effects
Keywords:
Space-fractional Stefan problem, self-similar Solution, diffusion-convection equation, comparison technique, fractional calculusAbstract
The fractional Stefan problem finds broad applicability 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. In this work, we study self-similar solutions of the space-fractional Stefan problem with diffusion-convection effects. By employing a rescaling technique together with a comparison theorem, the governing space-fractional diffusion-convection equation is reduced and reformulated for analysis. We then investigate the existence and structure of self-similar solutions expressed through the Mittag-Leffler function. Particular attention is given to qualitative properties, including nonnegativity, regularity, and the geometric shape of similarity profiles. The results demonstrate how the fractional order significantly influences front propagation and anomalous diffusion phenomena, offering new insights into fractional modeling of heat and mass transfer processes.
Mathematics Subject Classification (2010):26A33, 35C06, 35R11, 35R35, 80A22,
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