Abstract
In this article, we implement relatively analytical techniques such as the homotopy perturbation method and homotopy analysis method to solve nonlinear partial fractional differential Zakharov-Kuznetsov equations. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions obtained by the homotopy perturbation method and the approximate solutions obtained by homotopy analysis method. Also we make the figures compare between the approximate solutions. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when . Key words: Zakharov-Kuznetsov equations, the fractional derivatives, the homotopy perturbation method, the homotopy perturbation method, the approximate solutions.
Highlights
In recent years, fractional differential equations have gained much attention as they are widely used to describe various complex phenomena in many fields such as the fluid flow, signal processing, control theory, systems identification, biology and other areas
Many applications of fractional calculus can be found in turbulence and fluid dynamics, stochastic dynamical system, plasma physics and controlled thermonuclear fusion, nonlinear control theory, image processing, nonlinear biological systems and astrophysics (Kilbas et al, 2006; Podlubny, 1999; Samko et al, 1993; El-Sayed, 1996; Herzallah et al, 2010, 2011; Magin, 2006; West et al, 2003; Jesus and Machado, 2008; Agrawal and Baleanu, 2007; Tarasov, 2008)
We used the two different methods such as homotopy perturbation method and homotopy analysis method to obtain analytic approximate solutions for the fractional Zakharov-Kuznetsov equations which are very important in mathematical physics especially in nonlinear dynamics and plasma physics
Summary
Mathematics Department, Faculty of Science, Zagazig University, Egypt. Mathematics Department, Faculty of Science, Taif University, Saudi Arabia. Mathematics Department, Faculty of Science, El-Minia University, Egypt. We implement relatively analytical techniques such as the homotopy perturbation method and homotopy analysis method to solve nonlinear partial fractional differential ZakharovKuznetsov equations. The fractional derivatives are described in the Caputo sense. We compare between the approximate solutions obtained by the homotopy perturbation method and the approximate solutions obtained by homotopy analysis method. We make the figures compare between the approximate solutions. We compare between the approximate solutions and the exact solutions for the partial fractional differential equations when , , 1
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