Browsing by Author "Abdel-Aty, Abdel-Haleem"

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Citation - WoS: 38
Citation - Scopus: 46
Abundant Distinct Types of Solutions for the Nervous Biological Fractional Fitzhugh-Nagumo Equation Via Three Different Sorts of Schemes
(Springer, 2020) Khater, Mostafa M. A.; Baleanu, Dumitru; Khalil, E. M.; Bouslimi, Jamel; Omri, M.; Abdel-Aty, Abdel-Haleem; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana-Baleanu (AB) time-fractional FitzHugh-Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical evaluated solutions is illustrated based on the characteristics of the Hamiltonian to explain the applicability of them in the model's applications. Also, the physical and dynamical behaviors of the gained solutions are clarified by sketching them in three different types of plots. The practical side and power of applied methods are shown to explain their ability to use on many other nonlinear evaluation equations.
Accurate novel explicit complex wave solutions of the (2+1)-dimensional Chiral nonlinear Schrodinger equation
(2021) Alshahrani, B.; Yakout, H. A.; Khater, Mostafa M. A.; Abdel-Aty, Abdel-Haleem; Mahmoud, Emad E.; Baleanu, Dumitru; Eleuch, Hichem; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This manuscript investigates the accuracy of the solitary wave solutions of the (2+1)-dimensional nonlinear Chiral Schrodinger ((2+1)-D CNLS) equation that are constructed by employing two recent analytical techniques (modified Khater (MKhat) and modified Jacobian expansion (MJE) methods). This investigation is based on evaluating the initial and boundary conditions through the obtained analytical solutions then employing the Adomian decomposition (AD) method to evaluate the approximate solutions of the (2+1)-D CNLS equation. This framework gives the ability to get large complex traveling wave solutions of the considered model and shows the superiority of the employed computational schemes by comparing the absolute error for each of them. The handled model describes the edge states of the fractional quantum hall effect. Many novel solutions are obtained with various formulas such as trigonometric, rational, and hyperbolic to the studied model. For more illustration of the results, some solutions are displayed in 2D, 3D, and density plots.
Citation - WoS: 31
Citation - Scopus: 41
Oblique Explicit Wave Solutions of the Fractional Biological Population (Bp) and Equal Width (Ew) Models
(Springer, 2020) Khater, Mostafa M. A.; Baleanu, Dumitru; Abo-Dahab, S. M.; Bouslimi, Jamel; Omri, M.; Abdel-Aty, Abdel-Haleem; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This research uses the extended exp-(-phi(theta))-expansion and the Jacobi elliptical function methods to obtain a fashionable explicit format for solutions to the fragmented biological population and the same width models that depict popular logistics because of deaths or births. In mathematical terminology, the linear, hyperbolic, and trigonometric equation solutions that have been found describe several innovative aspects from the two models. Sketching these solutions in different types is used to give them more details. The accuracy and performance of the method adopted show their ability to be applied to various nonlinear developmental equations.