Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article Citation - WoS: 22Citation - Scopus: 26Exact Solutions for Fractional Ddes Via Auxiliary Equation Method Coupled With the Fractional Complex Transform(John Wiley and Sons Inc., 2016) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyDynamical 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: 21Citation - Scopus: 21An Analytic Approach To a Class of Fractional Differential-Difference Equations of Rational Type Via Symbolic Computation(John Wiley and Sons Inc., 2015) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyFractional 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: 17Citation - Scopus: 25The First Integral Method for Constructing Exact and Explicit Solutions To Nonlinear Evolution Equations(John Wiley and Sons Inc., 2012) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyProblems 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: 16Citation - Scopus: 15Constructing Rational and Multi-Wave Solutions To Higher Order Nees Via the Exp-Function Method(John Wiley and Sons Inc., 2011) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn 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: 9Citation - Scopus: 10Application of the Exp-Function Method To Nonlinear Lattice Differential Equations for Multi-Wave and Rational Solutions(John Wiley and Sons Inc., 2011) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyIn this paper, we extend the basic Exp-function method to nonlinear lattice differential equations for constructing multi-wave and rational solutions for the first time. We consider a differential-difference analogue of the Korteweg-de Vries equation to elucidate the solution procedure. Our approach is direct and unifying in the sense that the bilinear formalism of the equation studied becomes redundant.Article Citation - WoS: 6Citation - Scopus: 6Some Exact Solutions for Toda Type Lattice Differential Equations Using the Improved (g'/g)-expansion Method(John Wiley and Sons Inc., 2012) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyNonlinear lattice differential equations (also known as differential-difference equations) appear in many applications. They can be thought of as hybrid systems for the inclusion of both discrete and continuous variables. On the basis of an improved version of the basic (G′/G)- expansion method, we focus our attention towards some Toda type lattice differential systems for constructing further exact traveling wave solutions. Our method provides not only solitary and periodic wave profiles but also rational solutions with more arbitrary parameters. © 2012 John Wiley & Sons, Ltd.Article Citation - WoS: 10Citation - Scopus: 11The Discrete (g'/g)-expansion Method Applied To the Differential-Difference Burgers Equation and the Relativistic Toda Lattice System(John Wiley and Sons Inc., 2012) Aslan, İsmail; Aslan, İsmail; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyWe introduce the discrete (G′/G)-expansion method for solving nonlinear differential-difference equations (NDDEs). As illustrative examples, we consider the differential-difference Burgers equation and the relativistic Toda lattice system. Discrete solitary, periodic, and rational solutions are obtained in a concise manner. The method is also applicable to other types of NDDEs. © 2010 Wiley Periodicals, Inc.