Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 69Citation - Scopus: 69Optical Solitons and Modulation Instability Analysis of an Integrable Model of (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation(Academic Press Ltd- Elsevier Science Ltd, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper addresses the nonlinear Schrbdinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 17Citation - Scopus: 19Quasi Binormal Schrodinger Evolution of Wave Polarization Field of Light With Repulsive Type(Iop Publishing Ltd, 2021) Demirkol, Ridvan Cem; Khalil, Eied M.; Korpinar, Zeliha; Baleanu, Dumitru; Inc, Mustafa; Korpinar, TalatIn this paper, we study the evolution of the wave polarization vector in the tangent direction of the curved path. This path is assumed to be the trajectory of the propagated light beam. The polarization state of the wave is described by the unit complex transverse field component by eliminating the longitudinal field component. We obtain new relationship between the geometric phase and the parallel transportation law of the wave polarization vector of the evolving light beam in the tangent direction of the curved path. Moreover, we present a new geometric interpretation of the quasi binormal evolution of the wave polarization vector via the nonlinear Schrodinger equation of repulsive type in the tangent direction. Finally, we find a space-time nonlocal NLS reduction for equation system.Article Citation - WoS: 25Citation - Scopus: 26Optical Solitons and Modulation Instability Analysis With (3+1)-Dimensional Nonlinear Shrodinger Equation(Academic Press Ltd- Elsevier Science Ltd, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper addresses the (3 + 1)-dimensional nonlinear Shrodinger equation (NLSE) that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the solitary wave ansatz with Jaccobi elliptic function methods, we present the exact dark, bright and dark-bright or combined optical solitons to the model. The intensity as well as the nonlinear phase shift of the solitons are reported. The modulation instability aspects are discussed using the concept of linear stability analysis. The MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 16Citation - Scopus: 15On Numerical Solution of the Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu Derivative(Sciendo, 2019) Inc, Mustafa; Bayram, Mustafa; Baleanu, Dumitru; Partohaghighi, MohammadA powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): (ABC)D(0+)(,t)(beta)u(x, t) = zeta u(xx)(x, t) - kappa u(x)(x, t) + F(x, t), 0 < beta <= 1. The time-fractional derivative (ABC)D(0+)(,t)(beta)u(x, t) is described in the Atangana-Baleanu Caputo concept. The basis of our approach is transforming the original equation into a new equation by imposing a transformation involving a fictitious coordinate. Then, a geometric scheme namely the group preserving scheme (GPS) is implemented to solve the new equation by taking an initial guess. Moreover, in order to present the power of the presented approach some examples are solved, successfully.Article Citation - WoS: 6Citation - Scopus: 3Numerical 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.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.Article Citation - WoS: 180Citation - Scopus: 185New Solitary Wave Solutions for Variants of (3+1)-Dimensional Wazwaz-Benjamin Equations(Frontiers Media Sa, 2020) Inc, Mustafa; Baleanu, Dumitru; Rezazadeh, HadiWe solve distinct forms of (3+1)-Dimensional Wazwaz-Benjamin-Bona-Mahony [(3+1)-Dimensional WBBM] equations by employing the method of Sardar-subequation. When parameters involving this approach are taken to be special values, we can obtain the solitary wave solutions (sws) which is concluded from other approaches such as the functional variable method, the trail equation method, the first integral method and so on. We obtain new and general solitary wave solutions in terms of generalized hyperbolic and trigonometric functions. The results demonstrate the power of the proposed method for the determination of sws of non-linear evolution equations (NLEs).Article Citation - Scopus: 1Magnetic Charged Particles of Optical Spherical Antiferromagnetic Model With Fractional System(de Gruyter Poland Sp Z O O, 2021) Korpinar, Talat; Baleanu, Dumitru; Korpinar, Zeliha; Almohsen, Bandar; Inc, Mustafa; Yao, Shao-WenIn this article, we first consider approach of optical spherical magnetic antiferromagnetic model for spherical magnetic flows of Upsilon-magnetic particle with spherical de-Sitter frame in the de-Sitter space S-1(2). Hence, we establish new relationship between magnetic total phases and spherical timelike flows in de-Sitter space S-1(2). In other words, the applied geometric characterization for the optical magnetic spherical antiferromagnetic spin is performed. Moreover, this approach is very useful to analyze some geometrical and physical classifications belonging to Upsilon-particle. Besides, solutions of fractional optical systems are recognized for submitted geometrical designs. Geometrical presentations for fractional solu-tions are obtained to interpret the model. These obtained results represent that operation is a compatible and sig-nificant application to restore optical solutions of some fractional systems. Components of models are described by physical assertions with solutions. Additionally, we get solutions of optical fractional flow equations with designs of our results in de-Sitter space S-1(2).Article Citation - WoS: 4Citation - Scopus: 4Comparison Between the Thermoelectric Properties of New Materials: the Alloy of Iron, Vanadium, Tungsten, and Aluminum (Fe2v0.8w0.2al) Against an Oxide Such as Naco2o4(Elsevier Gmbh, 2021) Kaid, Noureddine; Ameur, Houari; Inc, Mustafa; Baleanu, Dumitru; Menni, Younes; Lorenzini, Giulio; Sifi, IbtissemAn analysis of the thermoelectric characteristics of certain recently discovered materials is carried out in this investigation. The alloy of iron, vanadium, tungsten, and aluminum (Fe2V0.8W0.2Al) applied to a silicon crystal is compared to new inorganic thermoelectric materials, which are mosly oxides like NaCO2O4. For both materials, the thermoelectric effects, Seebeck effect, Peltier effect, Thomson effect, and Kelvin relations are described. The cooling rate's influence on the energy balance is also assessed. The traditional thermoelectric materials provided are mostly made up of toxic, rare and/or expensive elements, which makes large-scale thermoelectric generator integration difficult. In recent decades, research has shifted toward the development of novel materials with a better price-to-performance ratio. Despite a low conversion yield, the family of oxides offers significant benefits in this respect, which are particularly evident at high temperatures. The findings of our study indicated that Fe2V0.8W0.2 applied to a silicon crystal has good thermoelectric characteristics. A sufficient merit factor was found in the new substance under investigation.Article Citation - WoS: 38Citation - Scopus: 39Combined Optical Solitary Waves and Conservation Laws For. Nonlinear Chen-Lee Equation in Optical Fibers(Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaThis paper obtains a combined optical solitary wave solution that is modeled by nonlinear Chen-Lee-Liu equation (NCLE) which arises in the context of temporal pulses along optical fibers associated with the self-steepening nonlinearity using the complex envelope function ansatz. The novel combined solitary wave describes bright and dark solitary wave properties in the same expression. The intensity and the nonlinear phase shift of the combined solitary wave solution are reported. Moreover, the Lie point symmetry generators or vector fields of a system of partial differential equations (PDEs) which is acquired by transforming the NCLE to a real and imaginary parts are derived. It is observed that the obtained system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conservation laws (Cis) for the system using the general Cls theorem. Numerical simulation and physical interpretations of the obtained results are demonstrated with interesting figures showing the meaning of the acquired results. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the NCLE. (C) 2017 Elsevier GmbH. All rights reserved.Article Citation - WoS: 24Citation - Scopus: 24Exact Optical Solitons of the Perturbed Nonlinear Schrodinger-Hirota Equation With Kerr Law Nonlinearity in Nonlinear Fiber Optics(de Gruyter Poland Sp Z O O, 2020) Abbagari, Souleymanou; Betchewe, Gambo; Inc, Mustafa; Doka, Serge Y.; Crepin, Kofane Timoleon; Almohsen, Bandar; Houwe, AlphonseThis article studies dark, bright, trigonometric and rational optical soliton solutions to the perturbed nonlinear Schrodinger-Hirota equation (PNLSHE). Hence, we have examined two cases: first, restrictions have been done to the third-order (TOD) (gamma) as constraint relation, and the coupling coefficients (sigma) is obtained as well as the velocity of the soliton by adopting the traveling wave hypothesis. Second, the TOD and the coupling coefficients are non-zero value, sending back to the PNLSHE, which has been studied in refs. [4,10,16] recently. By employing two relevant integration technics such as the auxiliary equation and the modified auxiliary equation method, miscellaneous optical solitary wave is obtianed, which is in agreement with the outcomes collected by the previous studies [4,16]. These results help in obtaining nonlinear optical fibers in the future.