Prof. Mohammed Abdalla Al-Refai
Yarmouk University, Irbid, Jordan
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Academic Career Length
24Years (2003-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications1 June 2019 in Chaos, Solitons & Fractals: X
Journal Article
Muhammed SyamMohammed Abdalla Al-Refai10 October 2017 in Advances in Difference Equations
Journal Article
Mohammed Abdalla Al-RefaiTAThabet Abdeljawad
Thabet AbdeljawadIn this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog. Fract. Differ. Appl. 1(2):73-85, 2015). We first derive simple and strong maximum principles for the linear fractional equation. We then implement these principles to establish uniqueness and stability results for the linear and nonlinear fractional diffusion problems and to obtain a norm estimate of the solution. In contrast with the previous results of the fractional diffusion equations, the obtained maximum principles are analogous to the ones with the Caputo fractional derivative; however, extra necessary conditions for the existence of a solution of the linear and nonlinear fractional diffusion models are imposed. These conditions affect the norm estimate of the solution as well.
14 September 2017 in Complexity
Journal Article
Mohammed Abdalla Al-RefaiTAThabet Abdeljawad
Thabet AbdeljawadWe suggest a regular fractional generalization of the well-known Sturm-Liouville eigenvalue problems. The suggested model consists of a fractional generalization of the Sturm-Liouville operator using conformable derivative and with natural boundary conditions on bounded domains. We establish fundamental results of the suggested model. We prove that the eigenvalues are real and simple and the eigenfunctions corresponding to distinct eigenvalues are orthogonal and we establish a fractional Rayleigh Quotient result that can be used to estimate the first eigenvalue. Despite the fact that the properties of the fractional Sturm-Liouville problem with conformable derivative are very similar to the ones with the classical derivative, we find that the fractional problem does not display an infinite number of eigenfunctions for arbitrary boundary conditions. This interesting result will lead to studying the problem of completeness of eigenfunctions for fractional systems.
2 January 2020 in Advances in Difference Equations
Journal Article
Mohammed Abdalla Al-RefaiIn this paper, we define the weighted Atangana–Baleanu fractional operators of Caputo sense. We obtain the solution of a related linear fractional differential equation in a closed form, and use the result to define the weighted Atangana–Baleanu fractional integral. We then express the weighted Atangana–Baleanu fractional derivative in a convergent series of Riemann–Liouville fractional integrals, and establish commutative results of the weighted Atangana–Baleanu fractional operators.
1 September 2019 in Chaos, Solitons & Fractals
Journal Article
Mohammed Abdalla Al-RefaiAJAbdulla M. Jarrah
Abdulla M. Jarrah
1 July 2011 in Nonlinear Analysis
Journal Article
Mohammed Abdalla Al-RefaiMHMohamed Ali Hajji
Mohamed Ali HajjiAbout Me
Mohammed Al-Refai earned his Ph.D. degree in Applied Mathematics from McGill University, Canada (2000); since then, he has held research and teaching positions at several institutions, namely, UAE University, Jordan University of Science and Technology, New York Institute of Technology, and McGill University. His research interests include numerical and analytical methods for ordinary and partial differential equations, maximum principle, fractional calculus, non-local problems, and financial mathematics. He has published more than 80 papers in peer reviewed journals with good reputations.
Prof. Al-Refai is the Editor-in-Chief of the Jordan Journal of Mathematics and Statistics. https://jjms.yu.edu.jo/index.php/jjms
He has been listed among the top 2% of researchers worldwide for five consecutive years (2021, 2022, 2023, 2024, and 2025), according to the Stanford University–Elsevier World’s Top 2% Scientists ranking. He received many research grants and participated in organizing several scientific meetings and delivered talks in more than 40 international scientific conferences in the area of applied mathematics. He has received over 2,000 citations on Google Scholar
https://scholar.google.com/citations?user=nRujkOYAAAAJ&hl=ar&oi=ao