Fractional Stefan problems

• Grant number: 18/05611-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: July 01, 2018
• End date: June 30, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Eliana Contharteze Grigoletto
• Grantee: Larissa Silva Zambrana Moraes
• Host Institution: Faculdade de Ciências Agronômicas (FCA). Universidade Estadual Paulista (UNESP). Campus de Botucatu. Botucatu , SP, Brazil

Abstract

In this project, we intend to solve a time-space fractional Stefan problem, appropriate approach to model anomalous diffusion, including fracional-order derivatives in time-space variables in the Fourier heat conduction equation. We consider the fractional time derivative of order alpha in (0,1] in the Caputo sense and fractional space derivative of order beta in (1,2], in the Riesz sense, with the presence of a space-fractional Laplacian. We note that the melt front advance as the square root of time in classical one-phase, melting Stefan problem, consistent with anomalous behaviors. Including time and space fractional derivatives, the melt front will advance as s~t^xi, where xi is a function of alpha and beta variables, then we can recover sub- and super-diffusion behaviors. (AU)