Analytical Method for solving fractional order generalized KdV Equation
by beta-fractional derivative
Abstract
The present work is related to solve the fractional generalized
Korteweg-de Vries (gKdV) equation in fractional time derivative form of
order alpha. Some exact solutions of the fractional-order gKdV equation
is attained by employing the new powerful expansion approach by using
the beta-fractional derivative which is used to get many solitary wave
solutions by changing the various parameters. 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.