Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 35Citation - Scopus: 34New 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, DumitruSardar 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.Article Citation - WoS: 23Citation - Scopus: 23The Generalized Sasa-Satsuma Equation and Its Optical Solitons(Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, MustafaThe principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa-Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa-Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.Article Citation - WoS: 2Citation - Scopus: 3On 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.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.Article On Solutions of Variable-Order Fractional Differential Equations(Elsevier B.V., 2017) Akgül, Ali; Inc, Mustafa; Baleanu, Dumitru; Abdalla, Bahaaeldin; Jarad, Fahd; Bouchelaghem, Faycal; Abdeljawad, Thabet; Ardjouni, Abdelouaheb; Boulares, Hamid; Shah, KamalNumerical calculation of the fractional integrals and derivatives is the code tosearch fractional calculus and solve fractional differential equations. The exactsolutions to fractional differential equations are compelling to get in real ap-plications, due to the nonlocality and complexity of the fractional differentialoperators, especially for variable-order fractional differential equations. There-fore, it is significant to enhance numerical methods for fractional differentialequations. In this work, we consider variable-order fractional differential equa-tions by reproducing kernel method. There has been much attention in theuse of reproducing kernels for the solutions to many problems in the recentyears. We give an example to demonstrate how efficiently our theory can beimplemented in practice.Article Citation - WoS: 7Citation - Scopus: 9Solitons and Complexitons To the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Model(World Scientific Publ Co Pte Ltd, 2019) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Aliyu, Aliyu IsaThis paper investigates the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified F-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.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: 3Citation - Scopus: 2On Fermi-Walker Transformation for Timelike Flows in Spacetime(Elsevier, 2021) Baleanu, Dumitru; Korpinar, Zeliha; Inc, Mustafa; Korpinar, TalatIn this manuscript, we firstly suggest different type for Fermi-Walker transportations along with flow lines of a non-vanishing vector field in Minkowski spacetime. Moreover, we construct the evolution equations of Frenet fields by Fermi-Walker derivative in Minkowski spacetime. Also, Fermi Walker parallelism is obtained the evolution equations of Frenet fields. Finally, we obtain some new results for flows by this new derivative in Minkowski spacetime. (C) 2021 Elsevier B.V. All rights reserved.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: 17Citation - Scopus: 17Geometric Phase for Timelike Spherical Normal Magnetic Charged Particles Optical Ferromagnetic Model(Taylor & Francis Ltd, 2020) Korpinar, Zeliha; Inc, Mustafa; Baleanu, Dumitru; Korpinar, TalatWe introduce the theory of optical spherical Heisenberg ferromagnetic spin of timelike spherical normal magnetic flows of particles by the spherical frame in de Sitter space. Also, the concept of timelike spherical normal magnetic particles is investigated, which may have evolution equations. Afterward, we reveal new relationships with some integrability conditions for timelike spherical normal magnetic flows in de-Sitter space. In addition, we obtain total phases for spherical normal magnetic flows. We also acquire perturbed solutions of the nonlinear Schrodinger's equation that governs the propagation of solitons in de-Sitter space S-1(2). Finally, we provide some numerical simulations to supplement the analytical outcomes.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.