Browsing by Author "Al-Refai, Mohammed"

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Citation - WoS: 8
Citation - Scopus: 10
Analytical Treatments To Systems of Fractional Differential Equations With Modified Atangana-Baleanu Derivative
(World Scientific Publ Co Pte Ltd, 2023) Syam, Muhammed I.; Baleanu, Dumitru; Al-Refai, Mohammed
The solutions of systems of fractional differential equations depend on the type of the fractional derivative used in the system. In this paper, we present in closed forms the solutions of linear systems involving the modified Atangana-Baleanu derivative that has been introduced recently. For the nonlinear systems, we implement a numerical scheme based on the collocation method to obtain approximate solutions. The applicability of the results is tested through several examples. We emphasize here that certain systems with the Atangana-Baleanu derivative admit no solutions which is not the case with the modified derivative.
Citation - WoS: 4
Citation - Scopus: 5
Comparison Principles of Fractional Differential Equations With Non-Local Derivative and Their Applications
(Amer inst Mathematical Sciences-aims, 2021) Baleanu, Dumitru; Al-Refai, Mohammed
In this paper, we derive and prove a maximum principle for a linear fractional differential equation with non-local fractional derivative. The proof is based on an estimate of the non-local derivative of a function at its extreme points. A priori norm estimate and a uniqueness result are obtained for a linear fractional boundary value problem, as well as a uniqueness result for a nonlinear fractional boundary value problem. Several comparison principles are also obtained for linear and nonlinear equations.
Citation - WoS: 102
Citation - Scopus: 115
On an Extension of the Operator With Mittag-Leffler Kernel
(World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Al-Refai, Mohammed
Dealing with nonsingular kernels is not an easy task due to their restrictions at origin. In this short paper, we suggest an extension of the fractional operator involving the Mittag-Leffler kernel which admits integrable singular kernel at the origin. New solutions of the related differential equations were reported together with some perspectives from the modelling viewpoint.