WoS İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Inc, MustafaPublisher: search.filters.publisher.Amer Scientific Publishers

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 1
    Optical Solitary Wave Solutions for the Conformable Perturbed Nonlinear Schrodinger Equation With Power Law Nonlinearity
    (Amer Scientific Publishers, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Gulsen, Selahattin; Baleanu, Dumitru; Inc, Mustafa
    In this study, we apply three integration schemes to extract optical soliton solutions for the conformable perturbed nonlinear Schrodinger equation (CPNLSE) with power law nonlinearity (PLN). The integration schemes that are used to carry out such solutions are Sine-Cosine (SC), generalized tanh (GT), and Ricatti-Bernoulli (RB) sub-ODE methods. The constraints conditions for the existence of the solutions are reported. The solutions are obtained using newly proposed fractional derivative called conformable derivative. Numerical simulations of some of the obtained solutions are also illustrated.
  • Article
    Citation - WoS: 2
    Optical Solitons for Complex Ginzburg-Landau Model With Beta Derivative in Nonlinear Optics
    (Amer Scientific Publishers, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
    In this paper, we present some new optical solitons for Complex Ginzburg-Landau equation (CGLE) involving Kerr Law in nonlinear optics. Two integration schemes which are extended Jacobi elliptic function (EJEF) and generalized projective ricatti (GPR) methods are applied to reach such solutions. The governing equation in the present paper involves beta derivative. The constraints conditions for the existence of soliton solutions are reported. Numerical simulations of some of the obtained solutions are illustrated.
  • Article
    Citation - WoS: 4
    Invariant Subspace and Lie Symmetry Analysis, Exact Solutions and Conservation Laws of a Nonlinear Reaction-Diffusion Murray Equation Arising in Mathematical Biology
    (Amer Scientific Publishers, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
    Reaction-diffusion type equations are seen as models of pattern formation in biology and chemistry. The concept of Lie symmetry and invariant subspace (ISM) methods play a vital role in the study of partial differential equations (PDEs). Lie symmetry method helps to derive point symmetries, symmetry algebra and exact solution by reducing the PDEs to and ordinary differential equation (ODEs), while the invariant subspace method determines an invariant subspace and construct exact solutions of the PDEs by also reducing the PDEs to ODEs. In this article, the two methods are applied to derive the exact solutions of a nonlinear reaction-diffusion murray equation appearing in mathematical biology. Several kinds of solutions of the model are presented, including topological, singular and exponential function solutions. We classify the conservation laws (Cls) of the model using the multipliers approach. The paper conclude by giving a comprehensive physical interpretations and comparative study of the results showing the molecular nature of the acquired solutions.
  • Article
    Citation - WoS: 3
    Solitons and Conservation Laws for the (2+1)-Dimensional Davey-Stewartson Equations With Conformable Derivative
    (Amer Scientific Publishers, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
    This research obtains some new solitons for the Davey-Stewartson equation (DSE) with conformable derivative. The well known projective Ricatti equation ansatz (PREA) is employed to reach such solitons. The constraints conditions for the existence of soliton solutions are reported. Moreover, the conservation laws (Cls) for the governing equation is studied via multiplier technique. Physical features of some solutions are illustrated in Figures 1-8.
  • Article
    Citation - WoS: 1
    An Analysis of Analytic and Approximate Solutions of the Nonlinear Foam-Drainage Equation and Its Applications
    (Amer Scientific Publishers, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
    In this study, the modified Kudryashov and Riccati-Bernoulli (sub-ODE) methods are applied to construct some analytical solutions of the nonlinear Foam-drainage equation which plays an important part in the formation and evolution of liquid foams. Kink type, singular and logarithmic function solutions are obtained. Then, the residual power series method (RPSM) is used to analyze the numerical behavior of the equation by considering all the exact solutions. We observed that the modified Kudryashov and Riccati Bernoulli sub-ODE methods are powerful techniques for finding the exact solutions to various nonlinear models. Also, the RPSM is efficient for examining numerical behavior of nonlinear models. Some interesting figures are shown to show the reliability of the methods.