New solutions for conformable fractional Nizhnik–Novikov–Veselov system via \(G'/G\) expansion method and homotopy analysis methods



The main purpose of this paper is to find the exact and approximate analytical solution of Nizhnik–Novikov–Veselov system which may be considered as a model for an incompressible fluid with newly defined conformable derivative by using \(G'/G\) expansion method and homotopy analysis method (HAM) respectively. Authors used conformable derivative because of its applicability and lucidity. It is known that, the NNV system of equations is an isotropic Lax integrable extension of the well-known KdV equation and has physical significance. Also, NNV system of equations can be derived from the inner parameter-dependent symmetry constraint of the KP equation. Then the exact solutions obtained by using \(G'/G\) expansion method are compared with the approximate analytical solutions attained by employing HAM.


Nizhnik–Novikov–Veselov system \(G'/G\) Expansion Conformable derivative Homotopy analysis method 

Mathematics Subject Classification

35R11 34A08 26A33 


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Science and Art FacultyMustafa Kemal UniversityHatayTurkey
  2. 2.Department of MathematicsCankaya University, Ankara, Türkiye and Institute of Space ScienceMagurele-BucharestRomania

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