WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Department: search.filters.department.Çankaya UniversitySubject: search.filters.subject.Conformable Derivative

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Now showing 1 - 10 of 26
  • Article
    Citation - WoS: 35
    Citation - Scopus: 34
    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
    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.
  • Article
    Citation - WoS: 9
    Various Optical Solutions To the (1+1)-Telegraph Equation With Space-Time Conformable Derivatives
    (Semnan Univ, 2021) Gasmi, Boubeker; Kessi, Arezki; Jarad, Fahd; Hammouch, Zakia
    This paper presents a new sub-equation method based on an auxiliary equation which is implemented via the well-known generalized Kudryashov method, to construct new traveling waves to the Telegraph equation with time and space conformable derivatives. To illustrate its effectiveness, it was tested for seeking traveling wave solutions to the (1+1)-Telegraph equation with space-time conformable derivatives. With the help of Maple Software we derive some new solitary waves solutions. It can be concluded that the proposed method is an accurate tool for solving several kind of nonlinear evolution equations.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 13
    Exact Solutions of Stochastic Kdv Equation With Conformable Derivatives in White Noise Environment
    (Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Ulutas, Esma
    In 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: 66
    Citation - Scopus: 79
    Structure 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, Mohammed
    Nonclassical 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: 12
    Citation - Scopus: 16
    Soliton Solutions of Nonlinear Boussinesq Models Using the Exponential Function Technique
    (Iop Publishing Ltd, 2021) Baleanu, Dumitru; Nawaz, Sidra; Rezazadeh, Hadi; Javeed, Shumaila
    This 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: 9
    Citation - Scopus: 13
    Quantization 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, Mohamed
    In 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: 34
    Citation - Scopus: 35
    On 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 Huy
    In 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.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 6
    On a Problem for the Nonlinear Diffusion Equation With Conformable Time Derivative
    (Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Zhou, Yong; Huu Can, Nguyen; Au, Vo Van
    In this paper, we study a nonlinear diffusion equation with conformable derivative: D-t((alpha)) u = Delta u = L(x, t; u(x, t)), where 0 < alpha < 1, (x, t) is an element of Omega x (0, T). We consider both of the problems: Initial value problem: the solution contains the integral I = integral(t)(0) tau(gamma) d tau (critical as gamma <= -1). Final value problem: not well-posed (if the solution exists it does not depend continuously on the given data). For the initial value problem, the lack of convergence of the integral I, for gamma <= -1. The existence for the solution is represented. For the final value problem, the Hadamard instability occurs, we propose two regularization methods to solve the nonlinear problem in case the source term is a Lipschitz function. The results of existence, uniqueness and stability of the regularized problem are obtained. We also develop some new techniques on functional analysis to propose regularity estimates of regularized solution.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Nonlinear Singular P-Laplacian Boundary Value Problems in the Frame of Conformable Derivative
    (Amer inst Mathematical Sciences-aims, 2021) Jarad, Fahd; Adjabi, Yassine; Abdeljawad, Thabet; Bouloudene, Mokhtar; Alqudah, Manar A.
    This paper studies a class of fourth point singular boundary value problem of p-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 15
    Extension of Perturbation Theory To Quantum Systems With Conformable Derivative
    (World Scientific Publ Co Pte Ltd, 2021) Rabei, Eqab M.; Al-Jamel, Ahmed; Baleanu, Dumitru; Al-Masaeed, Mohamed
    In this paper, the perturbation theory is extended to be applicable for systems containing conformable derivative of fractional order alpha. This is needed as an essential and powerful approximation method for describing systems with conformable differential equations that are difficult to solve analytically. The work here is derived and discussed for the conformable Hamiltonian systems that appears in the conformable quantum mechanics. The required alpha-corrections for the energy eigenvalues and eigenfunctions are derived. To demonstrate this extension, three illustrative examples are given, and the standard values obtained by the traditional theory are recovered when alpha = 1.