Application of a new method for nonlinear partial differential equations of fractional order arising in fluid mechanics

Document Type : Research Paper

Authors

1 Bryansk State University of Engineering and Technology, Russia.

2 M. Auezov South Kazakhstan University, Shymkent, Kazakhstan.

3 Russian State Social University, Moscow, Russia.

4 Kazan Federal University, Kazan, Russia.

5 Kuban State University, Krasnodar, Russia.

Abstract

In this work, we established some exact solutions for the (2+1)-dimensional Zakharov-Kuznetsov, KdV, and K(2,2) equations which are considered based on the improved Exp-function method, by utilizing Maple software. We use the fractional derivatives with fractional complex transform. We obtained new periodic solitary wave solutions. The obtained solutions include three classes of soliton wave solutions in terms of hyperbolic function, trigonometric function, and rational function solutions. The obtained solutions and the exact solutions are shown graphically, highlighting the effects of non-linearity. Many other such types of nonlinear equations arising in fluid dynamics and nonlinear phenomena.

Keywords

Main Subjects

Computational Methods for Differential Equations
Volume 13, Issue 1
January 2025
Pages 1-12

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History

  • Receive Date: 14 February 2024
  • Revise Date: 24 March 2024
  • Accept Date: 24 March 2024

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