Matematik Bölümü Yayın Koleksiyonu

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

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Scopus Q: search.filters.scopusQuartile.Q3Subject: search.filters.subject.Conformable Derivative

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  • Article
    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.
  • 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: 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.
  • Article
    Citation - WoS: 8
    A New Numerical Technique for Solving Fractional Partial Differential Equations
    (Univ Miskolc inst Math, 2018) Baleanu, Dumitru; Acan, Omer
    We propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the same time, conformable reduced differential transform method (CRDTM) for FPDEs is briefly given and a numerical comparison is made between this method and the newly introduced CADM. In applied science, CADM can be used as an alternative method to obtain approximate and analytical solutions for FPDEs as CRDTM. In this study, linear and non-linear three problems are solved by these two methods. In these methods, the obtained solutions take the form of a convergent series with easily computable algorithms. For the applications, the obtained results by these methods are compared to each other and with the exact solutions. When applied to FPDEs, it is seem that CADM approach produces easy, fast and reliable solutions as CRDTM. 2010 Mathematics Subject Classification: 34A08; 34K28