Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique(MDPI AG, 2020) Javeed, Shumaila; Waheed, Asif; Suleman, Muhammad; Baleanu, Dumitru; Atif, M.; Alimgeer, Khurram Saleem; Nawaz, SidraArticle Citation - Scopus: 25On the Geometric and Physical Properties of Conformable Derivative(Murat TOSUN, 2024) Has, A.; Yılmaz, B.; Baleanu, D.In this article, we explore the advantages geometric and physical implications of the conformable derivative. One of the key benefits of the conformable derivative is its ability to approximate the tangent at points where the classical tangent is not readily available. By employing conformable derivatives, alternative tangents can be created to overcome this limitation. Thanks to these alternative (conformable) tangents, physical interpretation can be made with alternative velocity vectors. Furthermore, the conformable derivative proves to be valuable in situations where the tangent plane cannot be defined. It enables the creation of alternative tangent planes, offering a solution in cases where the traditional approach falls short. Geometrically speaking, the conformable derivative carries significant meaning. It provides insights into the local behavior of a function and its relationship with nearby points. By understanding the conformable derivative, we gain a deeper understanding of how a function evolves and changes within its domain. A several examples are presented in the article to better understand the article and visualize the concepts discussed. These examples are accompanied by visual representations generated using the Mathematica program, aiding in a clearer understanding of the proposed ideas. By combining theoretical explanations, practical examples, and visualizations, this article aims to provide a comprehensive exploration of the advantages and geometric and physical implications of the conformable derivative. © MSAEN.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 - Scopus: 14The Effect of Deformation of Special Relativity by Conformable Derivative(Sociedad Mexicana de Fisica, 2022) Al-Masaeed, M.; Rabei, E.M.; Baleanu, D.; Al-Jamel, A.In this paper, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory are re-stated. Then, the addition of velocity laws are derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, the conformable Klein-Gordon equation, and conformable Dirac equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium. © 2022, Revista Mexicana de Fisica. All Rights Reserved.Article Green’s Function and an Inequality of Lyapunov-Type for Conformable Boundary Value Problem(Institute of Mathematics, 2021) Basua, D.; Jonnalagadda, J.M.; Baleanu, D.In this article, we consider a conformable boundary value problem associated with Robin type boundary conditions and present a Lyapunov-type inequality for the same. Further, we attain a lower bound on the smallest eigenvalue for the corresponding conformable eigenvalue problem using the established result, semi maximum norm and Cauchy– Schwartz inequality. © 2021, Institute of Mathematics. All rights reserved.Article Citation - WoS: 14Citation - Scopus: 13Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, EsmaIn this article, we have considered Wick-type stochastic Korteweg de Vries (KdV) equation with conformable derivatives. By the help of white noise analysis, Hermit transform and extended G/G-expansion method, we have obtained exact travelling wave solutions of KdV equation with conformable derivatives. We have applied the inverse Hermit transform for stochastic soliton solutions and then we have shown how stochastic solutions can be presented as Brownian motion functional solutions by an application example.Article Citation - WoS: 66Citation - Scopus: 79Structure of Optical Soliton Solution for Nonliear Resonant Space-Time Schrodinger Equation in Conformable Sense With Full Nonlinearity Term(Iop Publishing Ltd, 2020) Al-Smadi, Mohammed; Al-Omari, Shrideh; Baleanu, Dumitru; Momani, Shaher; Alabedalhadi, MohammedNonclassical quantum mechanics along with dispersive interactions of free particles, long-range boson stars, hydrodynamics, harmonic oscillator, shallow-water waves, and quantum condensates can be modeled via the nonlinear fractional Schrodinger equation. In this paper, various types of optical soliton wave solutions are investigated for perturbed, conformable space-time fractional Schrodinger model competed with a weakly nonlocal term. The fractional derivatives are described by means of conformable space-time fractional sense. Two different types of nonlinearity are discussed based on Kerr and dual power laws for the proposed fractional complex system. The method employed for solving the nonlinear fractional resonant Schrodinger model is the hyperbolic function method utilizing some fractional complex transformations. Several types of exact analytical solutions are obtained, including bright, dark, singular dual-power-type soliton and singular Kerr-type soliton solutions. Moreover, some graphical simulations of those solutions are provided for understanding the physical phenomena.Article Citation - WoS: 12Citation - Scopus: 16Soliton Solutions of Nonlinear Boussinesq Models Using the Exponential Function Technique(Iop Publishing Ltd, 2021) Baleanu, Dumitru; Nawaz, Sidra; Rezazadeh, Hadi; Javeed, ShumailaThis paper deals with the new analytical solutions of conformable nonlinear Boussinesq equations. Boussinesq equation is one of the important equation in the field of applied mathematics and engineering, particularly in optical fibers, plasma physics, fluid dynamics, signal processing, and shallow water etc. The focus of this paper is to obtain the new explicit solutions of conformable Boussinesq equations. Exponential function technique is employed to solve the considered models. The conformable properties are utilized to obtain new analytical solutions for this type of nonlinear Boussinesq equations. The new analytical solutions are acquired especially for the space-time boussinesq equation. The results are shown graphically. The obtained solutions can be useful for engineers and physicists to further analyze the phenomena. The implemented technique is valuable for finding new analytical solutions of nonlinear partial differential equations (PDEs).Article Citation - WoS: 9Citation - Scopus: 13Quantization of Fractional Harmonic Oscillator Using Creation and Annihilation Operators(de Gruyter Poland Sp Z O O, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, MohamedIn this article, the Hamiltonian for the conform-able harmonic oscillator used in the previous study [Chung WS, Zare S, Hassanabadi H, Maghsoodi E. The effect of fractional calculus on the formation of quantum-mechan-ical operators. Math Method Appl Sci. 2020;43(11):6950-67.] is written in terms of fractional operators that we called alpha-creation and alpha-annihilation operators. It is found that these operators have the following influence on the energy states. For a given order alpha, the alpha-creation operator pro-motes the state while the alpha-annihilation operator demotes the state. The system is then quantized using these crea-tion and annihilation operators and the energy eigenvalues and eigenfunctions are obtained. The eigenfunctions are expressed in terms of the conformable Hermite func-tions. The results for the traditional quantum harmonic oscillator are found to be recovered by setting alpha = 1.Article Citation - WoS: 34Citation - Scopus: 35On Well-Posedness of the Sub-Diffusion Equation With Conformable Derivative Model(Elsevier, 2020) Tran Bao Ngoc; Baleanu, Dumitru; O'Regan, Donal; Nguyen Huy Tuan; Ngoc, Tran Bao; Tuan, Nguyen HuyIn this paper, we study an initial value problem for the time diffusion equation (C)partial derivative(beta)/partial derivative t(beta) u + Au = F, 0 < beta <= 1, on Omega x (0, T), where the time derivative is the conformable derivative. We study the existence and regularity of mild solutions in the following three cases with source term F: F = F (x, t), i.e., linear source term; F = F (u) is nonlinear, globally Lipchitz and uniformly bounded. The results in this case play important roles in numerical analysis. F = F (u) is nonlinear, locally Lipchitz and uniformly bounded. The analysis in this case can be widely applied to many problems such as - Time Ginzburg-Landau equations C partial derivative(beta)u/partial derivative t(beta)+ (-Delta)u = vertical bar u vertical bar(mu-1) u; - Time Burgers equations C partial derivative(beta)u/partial derivative t(beta)-( u center dot del) u + (- Delta)u = 0; etc. (C) 2020 Elsevier B.V. All rights reserved.
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