Novel approximations to the fractional fifth-order KdV-type equations and modelling nonlinear structures arising in plasmas and fluid mechanics

This study aims to apply two highly effective and precise analytical methods: the Aboodh residual power series method and the Aboodh transform iterative method. These enhanced techniques are utilised to analyse and solve two types of fractional physical evolutionary wave equations including the planar fractional Kawahara equation and the planar fifth-order Korteweg–de Vries (FKdV) equation. The mentioned approaches are a mixed form of the standard Aboodh transform with the standard residual power series method and iterative method. Some highly accurate analytical approximate solutions are derived using the two proposed approaches. In these techniques, the generated approximations are expressed as convergent series solutions. All generated approximations are analysed both graphically and numerically to gain insight into the dynamics of the nonlinear phenomena they represent, including planar solitary waves. The absolute error is also computed to assess the generated approximations’ precision and validate the efficacy of the proposed approaches. The fractional evolutionary wave equations (EWEs) under study are widely used to analyse and model various nonlinear structures that emerge and propagate in fluid mechanics, plasma physics and optical physics. Consequently, the derived approximations are expected to reveal some behaviours not shown by the exact solutions of these equations in their integer cases.