Mathematics / Matematik
Permanent URI for this collectionhttps://hdl.handle.net/11147/8
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Article A Supplement To the Paper of Zayed Et Al. [optik, 170 (2018) 339-341](Elsevier, 2019) Aslan, İsmailIt seems that the results obtained by the so-called Khater method contain computational or print errors. We look at this issue from a different point of a view, namely, from a theoretical side. We prove our claim by a formal direct approach instead of back substitution (trial and error) approach.Article Traveling Waves of Ddes With Rational Nonlinearity(Walter de Gruyter GmbH, 2016) Aslan, İsmailIt has been found that the dynamical behavior of many complex physical systems can be properly described by nonlinear DDEs. However, in the related literature, research focusing on such equations with rational nonlinearity is rare. Hence, the present study makes an attempt to fill the existing gap. To this end, we consider two distinct DDEs with rational nonlinearity. We observed that the model equations assume three kinds of traveling wave solutions; hyperbolic, trigonometric and rational including kink-type solitary waves and singular periodic solutions. Our discussion is based on the auxiliary equation method.Article Citation - WoS: 14Citation - Scopus: 16Analytic Investigation of a Reaction-Diffusion Brusselator Model With the Time-Space Fractional Derivative(Walter de Gruyter GmbH, 2014) Aslan, İsmailIt is well known that many models in nonlinear science are described by fractional differential equations in which an unknown function appears under the operation of a derivative of fractional order. In this study, we propose a reaction-diffusion Brusselator model from the viewpoint of the Jumarie's modified Riemann-Liouville fractional derivative. Based on the (G'/G)-expansion method, various kinds of exact solutions are obtained. Our results could be used as a starting point for numerical procedures as well.Article Citation - WoS: 6Citation - Scopus: 4Remark 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, İsmailBy 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: 9Citation - Scopus: 9Multi-Wave and Rational Solutions for Nonlinear Evolution Equations(Walter de Gruyter GmbH, 2010) Aslan, İsmailNonlinear evolution equations always admit multi-soliton and rational solutions. The Burgers equation is used as an example, and the exp-function method is used to eluciadte the solution procedure.Article Citation - WoS: 9Citation - Scopus: 8Similarity Solutions To Burgers' Equation in Terms of Special Functions of Mathematical Physics(Jagellonian University, 2017) Öziş, Turgut; Aslan, İsmailIn this paper, the Lie group method is used to investigate some closed form solutions of famous Burgers' equation. A detailed and complete symmetry analysis is performed. By similarity transformations, the equation is reduced to ordinary differential equations whose general solutions are written in terms of the error function, Kummer's confluent hypergeometric function Φ(a; b; x) and Bessel functions Jp, showing the strong connection between the best mathematical modelling equations and the special functions of mathematical physics.Article Citation - WoS: 11Citation - Scopus: 12Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types(IOP Publishing Ltd., 2016) Aslan, İsmailDifferential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous. Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations, the majority of the results deal with polynomial types. Limited research has been reported regarding such equations of rational type. In this paper we present an adaptation of the (G′/G)-expansion method to solve nonlinear rational differential-difference equations. The procedure is demonstrated using two distinct equations. Our approach allows one to construct three types of exact traveling wave solutions (hyperbolic, trigonometric, and rational) by means of the simplified form of the auxiliary equation method with reduced parameters. Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.Article Citation - WoS: 36Citation - Scopus: 40Exact Solutions for a Local Fractional Dde Associated With a Nonlinear Transmission Line(IOP Publishing Ltd., 2016) Aslan, İsmailOf recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.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, İsmailDynamical 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: 15Citation - Scopus: 15Exact Solutions of a Fractional-Type Differential-Difference Equation Related To Discrete Mkdv Equation(IOP Publishing Ltd., 2014) Aslan, İsmailThe extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before.