In this paper, we consider the Kawahara equation in a bounded interval and with delay term one of boundary conditions. Using two different approaches, prove that system is exponentially stable under condition on length spatial domain. Specifically, first result obtained by introducing suitable energy functional using Lyapunov’s approach, to ensure goes 0 as $$t \rightarrow \infty $$ . The secon...

This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. method combines Zain Ul Abadin Zafar-transform (ZZ-T) and (HPT) show validation efficiency of this investigate three examples. It is also shown that fractional integer-order solutions have closed contact with exact result...

In this work, a damped modified Kawahara equation (mKE) with cubic nonlinearity and two dispersion terms including the third- fifth-order derivatives is analyzed. We employ an effective semi-analytical method to achieve goal set for study. For purpose, ansatz implemented find some approximate solutions mKE. Based on proposed method, different formulas analytical symmetric approximations are for...