Browsing by Author "Khater, Mostafa M. A."

Now showing 1 - 8 of 8

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.
Citation - WoS: 30
Citation - Scopus: 33
Abundant New Solutions of the Transmission of Nerve Impulses of an Excitable System
(Springer Heidelberg, 2020) Attia, Raghda A. M.; Baleanu, Dumitru; Khater, Mostafa M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This research investigates the dynamical behavior of the transmission of nerve impulses of a nervous system (the neuron) by studying the computational solutions of the FitzHugh-Nagumo equation that is used as a model of the transmission of nerve impulses. For achieving our goal, we employ two recent computational schemes (the extended simplest equation method and Sinh-Cosh expansion method) to evaluate some novel computational solutions of these models. Moreover, we study the stability property of the obtained solutions to show the applicability of them in life. For more explanation of this transmission, some sketches are given for the analytical obtained solutions. A comparison between our results and that obtained in previous work is also represented and discussed in detail to show the novelty for our solutions. The performance of the two used methods shows power, practical and their ability to apply to other nonlinear partial differential 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: 34
Citation - Scopus: 33
New Optical Solitons of Conformable Resonant Nonlinear Schrodinger's Equation
(de Gruyter Poland Sp Z O O, 2020) Rezazadeh, Hadi; Abazari, Reza; Khater, Mostafa M. A.; Inc, Mustafa; Baleanu, Dumitru; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Sardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrodinger's equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.
Citation - WoS: 6
Citation - Scopus: 3
Numerical Simulations for the Predator-Prey Model as a Prototype of an Excitable System
(Wiley, 2024) Almohsen, Bandar; Baleanu, Dumitru; Inc, Mustafa; Khater, Mostafa M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This research paper investigates the numerical solutions of the predator-prey model through five recent numerical schemes (Adomian decomposition, El Kalla, cubic B-spline, extended cubic B-spline, exponential cubic B-spline). We investigate the obtained computational solutions via the modified Khater methods. This model is considered as a well-known bimathematical model to describe the prototype of an excitable system. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. The accuracy of the obtained numerical solutions is investigated by calculating the absolute error between the exact and numerical solutions. Many sketches are given to illustrate the matching between the exact and numerical solutions.
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.
Citation - WoS: 42
Citation - Scopus: 34
On Abundant New Solutions of Two Fractional Complex Models
(Springer, 2020) Baleanu, Dumitru; Khater, Mostafa M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We use an analytical scheme to construct distinct novel solutions of two well-known fractional complex models (the fractional Korteweg-de Vries equation (KdV) equation and the fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation). A new fractional definition is used to covert the fractional formula of these equations into integer-order ordinary differential equations. We obtain solitons, rational functions, the trigonometric functions, the hyperbolic functions, and many other explicit wave solutions. We illustrate physical explanations of these solutions by different types of sketches.
Citation - WoS: 2
Citation - Scopus: 3
On Some Novel Optical Solitons To the Cubic-Quintic Nonlinear Helmholtz Model
(Springer, 2022) Inc, Mustafa; Tariq, Kalim U.; Tchier, Fairouz; Ilyas, Hamza; Baleanu, Dumitru; Khater, Mostafa M. A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The purpose of this study is to employ the Sine-Cosine expansion approach to produce some new sort of soliton solutions for the cubic-quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward scattering effects that are overlooked in the more popular nonlinear Schrodinger equation. As a result, a number of novel traveling wave structures have been discovered. We also investigate the stability of solitary wave solutions for the governing model. Furthermore, the modulation instability is discussed by employing the standard linear-stability analysis. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behaviour.