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    ANALYTICAL AND NUMERICAL SOLUTIONS FOR TIME-FRACTIONAL NEW COUPLED MKDV EQUATION ARISING IN INTERACTION OF TWO LONG WAVES
    (Asia Pacific Academic, 2019) Tasbozan, Orkun; Şenol, Mehmet; Kurt, Ali; Baleanu, Dumitru
    The aim of this paper is to present new exact solution sets of nonlinear conformable time-fractional new coupled mKdV equations which arise in interaction of two long waves with different dispersion relations by means of sub-equation method. In addition, we also propose an analytical-approximate method namely residual power series method (RPSM) for the system. The fractional derivatives have been explained in newly defined conformable type, during the solution procedure. The exact solutions of the system obtained by the sub-equation method have been compared to approximate solutions derived by RPSM. The results showed that both methods are robust, dependable, easy to apply and a good alternative for seeking solutions of fractional partial differential equations. © 2019 Asia Pacific Journal of Mathematics.
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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.