Overview:

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 is Brownian, 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.

Group Leader: Dr. Sebti Kerbal
Email: skerbal@squ.edu.om
Group members
Local:
Dr. Hanifa Mohamed Nasir, Sultan Qaboos University
Dr. Nasser Al Salti, National University of Science and technology, Oman
Prof. Samir Karaa, Sultan Qaboos University
Dr. Sebti Kerbal, Sultan Qaboos University
Dr. Fatma Al Musalhi, Sultan Qaboos University
Dr. Mariam Al Maskari, Sultan Qaboos University
International:
Dr. Ahmad Fino, American University of Middle East, Kuwait
Dr. Arran Fernandez, Eastern Mediterranean University Cyprus
Dr. Erkinjon Karimov, Ghent University, Belgium and Fergana State University, Uzbekistan

The multi-disciplinary research focuses on the modeling, simulation and characterization of nanofluids flow, heat and mass transfers in various media identifying their applications in physics, engineering, nanoscience and nanotechnology. The group actively works on various problems on nanofluids, prepare and submit projects for internal and external funding, jointly supervise PhD and MSc students, establish institutional collaboration nationally and internationally etc. Due to the excellent contributions in nanofluids research, the group was awarded the Most Active Research Group Award 2019 by the Deanship of Research, SQU. For the first time in history, receiving this award glorified the mathematics department as well as the College of Science.

Publications:

Latifa M. Al-Balushi, M. J. Uddin, M. M. Rahman, H. F. Oztop, I. Pop: Three‐dimensional tilted hydromagnetic natural double‐diffusive convection in a rectangular cuboid filled with nanofluids based on magnetic nanoparticles, Heat Transfer, vol. 51(2), pp. 1275-1305, 2022.

M. M. Rahman, M. S. Alam, N. Al-Salti, I. A. Eltayeb: Hydromagnetic natural convective heat transfer flow in an isosceles triangular cavity filled with nanofluid using two-component nonhomogeneous model, International Journal of Thermal Sciences, vol. 107, pp. 272-288, 2016.

Group Leader: Prof. Mohammad Mansur Rahman

Group members: Professor Mohammad Mansur Rahman, Sultan Qaboos University, Dr. Nasser Al Salti, National University of Science & Technology, Professor Md. Shariful Alam, Jagannath University, Dr. Khamis Al Kalbani, Sohar University, Dr. Md. Jashim Uddin, International Maritime College Oman, Dr. Sheikha Al-Weheibi, Sultan Qaboos University, Dr. Latifa Al-Balushi, Sultan Qaboos University