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    Functional Variable Method for conformable fractional modified KdV-ZK equation and Maccari system
    (Tbilisi Centre Math Sci, 2017) Cenesiz, Yucel; Tasbozan, Orkun; Kurt, Ali
    Modeling 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.
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    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, Dumitru
    Modelling 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.
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    New exact solutions of Burgers' type equations with conformable derivative
    (Taylor & Francis Ltd, 2017) Cenesiz, Yucel; Baleanu, Dumitru; Kurt, Ali; Tasbozan, Orkun
    In 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.
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    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, Ali
    In 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.
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    On the Solution of Burgers' Equation with the New Fractional Derivative
    (Sciendo, 2015) Kurt, Ali; Cenesiz, Yucel; Tasbozan, Orkun
    Firstly 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.
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    The solutions of time and space conformable fractional heat equations with conformable Fourier transform
    (De Gruyter Open Ltd, 2015) Cenesiz, Yucel; Kurt, Ali
    In this paper our aim is to find the solutions of time and space fractional heat differential equations by using new definition of fractional derivative called conformable fractional derivative. Also based on conformable fractional derivative definition conformable Fourier Transform is defined. Fourier sine and Fourier cosine transform definitions are given and space fractional heat equation is solved by conformable Fourier transform.
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    Stochastic solutions of conformable fractional Cauchy problems
    (Elsevier, 2017) Cenesiz, Yucel; Kurt, Ali; Nane, Erkan
    In this paper we give stochastic solutions of conformable fractional Cauchy problems. The stochastic solutions are obtained by running the processes corresponding to Cauchy problems with nonlinear deterministic clocks. Published by Elsevier B.V.