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Öğe Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system(TBILISI CENTRE MATH SCI, 2017) Cenesiz, Yucel; Tasbozan, Orkun; Kurt, AliModeling the motion and propagation characteristics of waves have importance in coastal, ocean and maritime engineering. Especially, waves are the major source of environmental actions on beaches or on man-made fixed or floating structures in most, geographical areas. So Maccari system has great application in mentioned areas. The modified KdV is ion acoustic perturbations evolution model in a plasma with two negative ion components which have different temperatures. As for the KdV equation, the modified ZK (mZK) equation arises naturally as weakly two-dimensional variations of the mKdV equation. hi this paper authors used functional variable method(FVM) for the first time to obtain exact travelling wave and soliton solutions of conformable fractional modified KdV-Zakharov-Kuznetsov(mKdv-ZK) equation and Maccari system. As a consequence, new solutions are obtained and it is seen that FVM is an valuable and efficient tool for solving nonlinear equations and systems where the derivatives defined by means of conformable fractional derivative.Öğe New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method(DE GRUYTER POLAND SP ZOO, 2017) Tasbozan, Orkun; Cenesiz, Yucel; Kurt, Ali; Baleanu, DumitruModelling of physical systems mathematically, produces nonlinear evolution equations. Most of the physical systems in nature are intrinsically nonlinear, therefore modelling such systems mathematically leads us to nonlinear evolution equations. The analysis of the wave solutions corresponding to the nonlinear partial differential equations (NPDEs), has a vital role for studying the nonlinear physical events. This article is written with the intention of finding the wave solutions of Nizhnik-Novikov-Veselov and Klein-Gordon equations. For this purpose, the exp-function method, which is based on a series of exponential functions, is employed as a tool. This method is an useful and suitable tool to obtain the analytical solutions of a considerable number of nonlinear FDEs within a conformable derivative.Öğe New exact solutions of Burgers' type equations with conformable derivative(TAYLOR & FRANCIS LTD, 2017) Cenesiz, Yucel; Baleanu, Dumitru; Kurt, Ali; Tasbozan, OrkunIn this paper, the new exact solutions for some nonlinear partial differential equations are obtained within the newly established conformable derivative. We use the first integral method to establish the exact solutions for time-fractional Burgers' equation, modified Burgers' equation, and Burgers-Korteweg-de Vries equation. We report that this method is efficient and it can be successfully used to obtain new analytical solutions of nonlinear FDEs.Öğe A New Method to Solve Time Fractional Diffusion Equations Arising in Chaos and Heat Conduction(AMER SCIENTIFIC PUBLISHERS, 2018) Ozkan, Ozan; Kurt, Ali; Tasbozan, OrkunThe goal of the present paper is to construct a method to obtain the solution of conformable fractional partial differential equations (CFPDEs). Since these systems can be transformed to partial differential equations (PDEs) by using wave transform, the reduced system can be solved by using differential transform method (DTM) solution methods. Based on this idea, we build an efficient solution procedure that reduces CFPDEs to PDEs via wave transform, then approximate the solution of obtained system by using Differential Transform Method (DTM) which is a special procedure for solving PDEs. As an example, we implement the method to time fractional Diffusion Equation (TFDE).Öğe New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method(SPRINGER HEIDELBERG, 2016) Tasbozan, Orkun; Cenesiz, Yucel; Kurt, AliIn this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.Öğe New solutions of fractional Drinfeld-Sokolov-Wilson system in shallow water waves(PERGAMON-ELSEVIER SCIENCE LTD, 2018) Tasbozan, Orkun; Senol, Mehmet; Kurt, Ali; Ozkan, OzanIn this paper, we present new exact solution sets of nonlinear conformable time-fractional coupled Drinfeld-Sokolov-Wilson equation which arise in shallow water flow models, when special assumptions are used to simplify the shallow water equations by means of Sine-Gordon expansion method. We also present an analytical approximate method namely perturbation-iteration algorithm (PIA) for the system. Basic definitions of fractional derivatives are described in the conformable sense. An example is given and the results are compared to exact solutions. The results show that the presented methods are powerful, reliable, simple to use and ready to apply to wide range of fractional partial differential equations.Öğe On the Solution of Burgers' Equation with the New Fractional Derivative(SCIENDO, 2015) Kurt, Ali; Cenesiz, Yucel; Tasbozan, OrkunFirstly in this article, the exact solution of a time fractional Burgers' equation, where the derivative is conformable fractional derivative, with dirichlet and initial conditions is found by Hopf-Cole transform. Thereafter the approximate analytical solution of the time conformable fractional Burger's equation is determined by using a Homotopy Analysis Method(HAM). This solution involves an auxiliary parameter (h) over bar which we also determine. The numerical solution of Burgers' equation with the analytical solution obtained by using the Hopf-Cole transform is compared.
