ABSTRACT
In chapter 5, the exact solutions for the space-time fractional Zakharov-Kuznetsev (ZK) equation, space-time fractional modified Zakharov-Kuznetsev (mZK) equation, time-fractional (3 + 1)-dimensional Korteweg-de Vries (KdV)-Zakharov-Kuznetsev, and space-time fractional (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsev equations have been successfully analyzed. By using the fractional sub-equation method, three types of exact analytical solutions including the generalized hyperbolic function solutions, generalized trigonometric function solutions, and rational solution for the space-time fractional Zakharov-Kuznetsev equation and two types exact analytical solutions including the generalized hyperbolic function solutions and generalized trigonometric function solutions for the space-time fractional mZK equation have been analyzed. Furthermore, the improved fractional sub-equation method has also been applied for getting the hyperbolic, trigonometric, and rational function form involving some parameters for time-fractional (3 + 1)-dimensional KdV-Zakharov-Kuznetsev and space-time fractional (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsev equations.
