Coordinator: Dr. Sebti Kerbal / College of Science  

Abstract:

FracDiff group is a multidisciplinary and interdisciplinary oriented research group constituted of junior and senior researchers including local and international members with expertise in the theory and computation of fractional differential equations (FDEs) and their applications.
Recent studies and experiments in various fields have shown the limitation of the classical theory of differential equations in describing phenomena that are non-local in time and/or space. This led to the birth of new field of studies, namely anomalous systems which are governed by FDE. Fractional differential models have received considerable attention in recent years, from both
practical and theoretical points of view, due to their great efficiency in capturing the dynamics of physical processes involving anomalous diffusion and transport phenomena. Among other problems arising in transport mechanisms, Diffusion represents interesting phenomena. The classical diffusion theory resides on the assumption that the underlying particle motion isBrownian, which predicts a linear growth with time for the mean squared deviation of the particle displacement. However, recent studies and experiments have shown that the corresponding mathematical model is governed by an integro-differential equation modeling anomalous diffusion,
instead of the usual diffusion equation. Recently, several numerical methods have been proposed with different types of spatial and temporal
discretizations. The main challenges in designing robust numerical schemes and in carrying out a rigorous error analysis stems from the non-locality of the fractional-order derivatives, and the associated limited smoothing properties. FracDiff research group will contribute to the field of fractional differential equations by studying the theory, modeling and computation of various problems.

Our research interest is to study questions related to existence, stability, convergence and efficient computational methods for various non-linear fractional differential models. Thereby, we explore and apply the obtained results to ground water modeling, viscoelastic, non Newtonian fluids, direct and inverse problems.