Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - Scopus: 14
The 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.
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.
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.
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.
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).
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.
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.
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.
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.
Citation - Scopus: 6
Computational Solutions of Conformable Space-Time Derivatives Dynamical Wave Equations: Analytical Mathematical Techniques
(Elsevier B.V., 2020) Seadawy, A.R.; Baleanu, D.; Ali, A.
In this article, the instigator sets up the profuse traveling wave solutions four types of fractional nonlinear equations in the sense of conformable derivatives by using the novel form of modified mathematical technique. The constructed traveling wave solutions are articulated in terms of trigonometric, hyperbolic and exponential functions. The derived results are fruitful for the physical demonstrations of problems in mathematical physics and engineering. © 2020 The Authors

Matematik Bölümü Yayın Koleksiyonu

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