Abstract
In this article, a modified method called the Elzaki decomposition method has been applied to analyze time-fractional Zakharov–Kuznetsov equations. In this method, the Adomian decomposition technique and Elzaki transformation are combined. Two problems are investigated to show and validate the efficiency of the suggested method. It is also shown that the solutions achieved from the current producer are in good contact with the exact solutions to show with the help of graphs and table. It is observed that the suggested technique is to be reliable, efficient, and straightforward to implement for many related models of engineering and science.
Highlights
Nonlinear fractional partial differential equations play important role in demonstrating different physical appearances identified with solid-state physics, fluid mechanics, chemical kinetics, population dynamics, plasma physics, nonlinear optics, protein chemistry, soliton theory, etc. ese nonlinear problems, just as their scientific arrangements, are of tremendous enthusiasm for suitable subjects
E Zakharov–Kuznetsov (ZK) equation is an extremely appealing model equation for investigating vortices in geophysical streams. e ZK problems show up in numerous regions of material science, implemented arithmetic, and designing. It appears in the territory of quantum physics [5,6,7,8,9]. e ZK problems administer the conduct of feebly nonlinear particle acoustic plasma waves, including cold particles and hot isothermal electrons within sight of a smooth magnetic field [10, 11]
Solitary wave arrangements were produced by determining the nondirect higher order of broadened KdV conditions for the free surface removal [12]
Summary
Nonlinear fractional partial differential equations play important role in demonstrating different physical appearances identified with solid-state physics, fluid mechanics, chemical kinetics, population dynamics, plasma physics, nonlinear optics, protein chemistry, soliton theory, etc. ese nonlinear problems, just as their scientific arrangements, are of tremendous enthusiasm for suitable subjects. The precise expository structures of some nonlinear advancement equations in numerical material science, to be specific, space timefractional Zakharov–Kuznetsov and modified Zakharov–Kuznetsov equations, were obtained [13]. It has been investigated in the past decades by many with the Complexity techniques such as new iterative Sumudu transform method [14], homotopy perturbation transform method [15], extended direct algebraic method [16], natural decomposition method, and q-homotopy analysis transform method [17]. The results of time-fractional equations and integral-order equations are investigated. e given method is very helpful in solving other fractional-order of PDEs
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