Obtaining new soliton solutions of the fractional generalized perturbed KdV equation

Abstract In this study, the fractional generalized perturbed KdV equation (gpKdV) with beta derivative is considered. The generalized exponential rational function method (GERFM) is applied to this equation for the first time in this study. Thus, dark soliton, bright soliton, singular soliton, mixed soliton, trigonometric function, rational trigonometric function, hyperbolic function and rational exponential function solutions of this fractional equation are obtained for the first time in this study. The 2D, 3D, and density plots, which effectively illustrate the behavior of these solitons, are shown for various values and specific ranges of the solutions.