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

Kazakov O. Uteuliyev N. Denisova D. Shangaraeva L. Vukovich G.
January 2025 University of Tabriz

Computational Methods for Differential Equations
2025 #13 Issue 1 1 - 12 pp.

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.

2) , Exp-function method(EFM) , K(2 , KdV , Zakharov-Kuznetsov

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Bryansk State University of Engineering and Technology, Russian Federation
M. Auezov South Kazakhstan University, Shymkent, Kazakhstan
Russian State Social University, Moscow, Russian Federation
Kazan Federal University, Kazan, Russian Federation
Kuban State University, Krasnodar, Russian Federation

Bryansk State University of Engineering and Technology
M. Auezov South Kazakhstan University
Russian State Social University
Kazan Federal University
Kuban State University

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