Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Institution Author: search.filters.institutionAuthor.Aslan, İsmailWoS Q: search.filters.wosQuartile.Q1

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Now showing 1 - 10 of 25
  • Article
    Citation - WoS: 6
    Citation - Scopus: 4
    Remark On:"exp-Function Method for the Exact Solutions of Fifth Order Kdv Equation and Modified Burgers Equation" [appl. Math. Comput. (2009) Doi:10.1016/J.amc.2009.07.009]
    (Elsevier Ltd., 2010) Aslan, İsmail
    By means of the Exp-function method, Inan and Ugurlu [Appl. Math. Comput. (2009) doi:10.1016/j.amc.2009.07.009] reported eight expressions for being solutions to the two equations studied. In fact, all of them can be easily simplified to constants.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 26
    Exact Solutions for Fractional Ddes Via Auxiliary Equation Method Coupled With the Fractional Complex Transform
    (John Wiley and Sons Inc., 2016) Aslan, İsmail
    Dynamical behavior of many nonlinear systems can be described by fractional-order equations. This study is devoted to fractional differential–difference equations of rational type. Our focus is on the construction of exact solutions by means of the (G'/G)-expansion method coupled with the so-called fractional complex transform. The solution procedure is elucidated through two generalized time-fractional differential–difference equations of rational type. As a result, three types of discrete solutions emerged: hyperbolic, trigonometric, and rational. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
  • Article
    Citation - WoS: 21
    Citation - Scopus: 21
    An Analytic Approach To a Class of Fractional Differential-Difference Equations of Rational Type Via Symbolic Computation
    (John Wiley and Sons Inc., 2015) Aslan, İsmail
    Fractional derivatives are powerful tools in solving the problems of science and engineering. In this paper, an analytical algorithm for solving fractional differential-difference equations in the sense of Jumarie's modified Riemann-Liouville derivative has been described and demonstrated. The algorithm has been tested against time-fractional differentialdifference equations of rational type via symbolic computation. Three examples are given to elucidate the solution procedure. Our analyses lead to closed form exact solutions in terms of hyperbolic, trigonometric, and rational functions, which might be subject to some adequate physical interpretations in the future. Copyright © 2013 JohnWiley & Sons, Ltd.
  • Article
    Citation - WoS: 18
    Citation - Scopus: 17
    Symbolic Computation of Exact Solutions for Fractional Differential-Difference Equation Models
    (Vilnius University Press, 2014) Aslan, İsmail
    The aim of the present study is to extend the (G′=G)-expansion method to fractional differential-difference equations of rational type. Particular time-fractional models are considered to show the strength of the method. Three types of exact solutions are observed: hyperbolic, trigonometric and rational. Exact solutions in terms of topological solitons and singular periodic functions are also obtained. As far as we are aware, our results have not been published elsewhere previously.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 25
    The First Integral Method for Constructing Exact and Explicit Solutions To Nonlinear Evolution Equations
    (John Wiley and Sons Inc., 2012) Aslan, İsmail
    Problems that are modeled by nonlinear evolution equations occur in many areas of applied sciences. In the present study, we deal with the negative order KdV equation and the generalized Zakharov system and derive some further results using the so-called first integral method. By means of the established first integrals, some exact traveling wave solutions are obtained in a concise manner.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 26
    On the Application of the Exp-Function Method To the Kp Equation for N-Soliton Solutions
    (Elsevier, 2012) Aslan, İsmail
    We observe that the form of the Kadomstev-Petviashvili equation studied by Yu (2011) [S. Yu, N-soliton solutions of the KP equation by Exp-function method, Appl. Math. Comput. (2011) doi:10.1016/j.amc.2010.12.095] is incorrect. We claim that the N-soliton solutions obtained by means of the basic Exp-function method and some of its known generalizations do not satisfy the equation considered. We emphasize that Yu's results (except only one) cannot be solutions of the correct form of the Kadomstev-Petviashvili equation. In addition, we provide some correct results using the same approach.
  • Article
    Comment On: the (g'/g)-expansion Method for the Nonlinear Lattice Equations [commun Nonlinear Sci Numer Simulat 17 (2012) 3490-3498]
    (Elsevier, 2012) Aslan, İsmail
    We show that two of the nonlinear lattice equations studied by Ayhan & Bekir [Commun Nonlinear Sci Numer Simulat 17 (2012) 3490-3498] have already been investigated by Aslan [Commun Nonlinear Sci Numer Simulat 15 (2010) 1967-1973] using an improved version of the same method. The solutions obtained by the latter one include the solutions obtained by the former one. © 2012 Elsevier B.V.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 16
    Comment On: "application of Exp-Function Method for (3+1 )-Dimensional Nonlinear Evolution Equations" [comput. Math. Appl. 56 (2008) 14511456]
    (Elsevier Ltd., 2011) Aslan, İsmail
    We show that Boz and Bekir [A. Boz, A. Bekir, Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations, Comput. Math. Appl. 56 (2008) 14511456] obtained some incorrect solutions for the equations studied by means of the Exp-function method. We verify our assertion by direct substitution and pole order analysis. In addition, we provide the correct results using the same approach.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 15
    Constructing Rational and Multi-Wave Solutions To Higher Order Nees Via the Exp-Function Method
    (John Wiley and Sons Inc., 2011) Aslan, İsmail
    In this paper, we present an application of some known generalizations of the Exp-function method to the fifth-order Burgers and to the seventh-order Korteweg de Vries equations for the first time. The two examples show that the Exp-function method can be an effective alternative tool for explicitly constructing rational and multi-wave solutions with arbitrary parameters to higher order nonlinear evolution equations. Being straightforward and concise, as pointed out previously, this procedure does not require the bilinear representation of the equation considered.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 34
    Exact and Explicit Solutions To Nonlinear Evolution Equations Using the Division Theorem
    (Elsevier Ltd., 2011) Aslan, İsmail
    In this paper, we show the applicability of the first integral method, which is based on the ring theory of commutative algebra, to the regularized long-wave Burgers equation and the Gilson-Pickering equation under a parameter condition. Our method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are derived in a concise manner.