Browsing by Author "Hammouch, Z."

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Citation Count: Bououden, R...at all (2021). "A novel fractional piecewise linear map: regular and chaotic dynamics", International Journal of General Systems, Vol. 50, No. 5, pp. 501-526.
A novel fractional piecewise linear map: regular and chaotic dynamics
(2021) Bououden, R.; Abdelouahab, M. S.; Jarad, Fahd; Hammouch, Z.; 234808
In this paper, a new piecewise linear map of the plan and its fractional version deduced from the Lozi map is introduced and analysed. The main attention is paid to the study of fixed points and their stability, cycles of period two and their stability regions and the type of bifurcation that occur in the dynamical behaviours of this map. The routes to chaos and some chaotic attractors that exist in the behaviour of the integer map are discussed. Finally, the chaotic behaviour of the associated proposed fractional map is analysed by means of bifurcations diagrams.
Citation Count: Abdeljawad, T...at all (2020). "A special issue:Recent developments in nonlinear partial differential equations", Advances in the Theory of Nonlinear Analysis and its Applications, Vol. 4, No. 4, pp. 214-215.
A special issue:Recent developments in nonlinear partial differential equations
(2020) Abdeljawad, T.; Al-Mdallal, Q.M; Hammouch, Z.; Jarad, F.; F.
The literature reveals that numerous real-life phenomena in the subjects of physics and engineering which are governed by highly nonlinear Partial differential equations (PDEs) with unknown analytical solutions. More precisely, the (PDEs) arise in a wide variety of physical problems such as; by way of example not exhaustive enumeration, fluid dynamics, engineering mathematics, electrostatics, plasma physics, solid mechanics, chemistry, quantum field theory, bio-mathematics, etc. Therefore, such (PDEs) have received a huge attention from mathematicians, physicists, and engineers for the sake of approximating their analytical solutions. We aimed in this special issue to publish articles focusing on recent advanced numerical studies on Differential Equations related to physics and engineering. The well-developed analysis of existing numerical algorithms in terms of efficiency, applicability, convergence, stability and accuracy is of importance. A discussion of nontrivial numerical examples is encouraged.
Citation Count: Uddin, M.F...et al. (2021). "Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods", Alexandria Engineering Journal, Vol. 60, No. 1, pp. 1055-1065.
Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods
(2021) Uddin, M.F.; Hafez, M.G.; Hammouch, Z.; Rezazadeh, H.; Baleanu, Dumitru; 56389
This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials.