Abstract
Abstract In this work, we consider the (3+1) dimensional conformable fractional Zakharov-Kuznetsov equation with power law nonlinearity. Solitary wave solutions, soliton wave solutions, elliptic wave solutions, and periodic (hyperbolic) wave rational solutions are obtained by means of the unified method. The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences.
Highlights
Nonlinear fractional partial di erential equations (FPDEs) show a rich variety of nonlinear phenomena, arise in many physical and engineering applications like geophysical uid mechanics, uid mechanics, plasma physics, superconductivity, and optics
Soliton wave solutions, elliptic wave solutions, and periodic wave rational solutions are obtained by means of the uni ed method
The solutions showed that this method provides us with a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various elds of applied sciences
Summary
Nonlinear fractional partial di erential equations (FPDEs) show a rich variety of nonlinear phenomena, arise in many physical and engineering applications like geophysical uid mechanics, uid mechanics, plasma physics, superconductivity, and optics. The conformable fractional derivatives didn’t have a physical meaning as the Caputo or Riemann-Liouville derivatives This situation is a general open problem for fractional calculus. Many researchers established exact traveling wave solutions of various nonlinear fractional evolution equations via this fractional derivative. Korkmaz [22] applied modi ed Kudryashov method to obtain the exact solutions of the the (3+1) conformable time-fractional Jimbo-Miwa, Zakharov-Kuznetsov and Modi ed ZakharovKuznetsov equations. Aminikhah et al [23] used the sub equation method to obtain the exact solutions of the fractional (1+1) and (2+1) regularized long-wave equations which arise in several physical applications, including ion sound waves in plasma. Rezazadeh et al [24, 25] concerned about the same method for obtaining traveling wave solutions for the conformable fractional generalized Kuramoto-Sivashinsky equation and fractional ZakharovKuznetsov equation with dual-power law nonlinearity. Tariq et al [26] investigated the new exact solutions of a nonlinear evolution equation that appear in mathematical physics, speci cally Cahn-Allen equation by applying
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