Finite-Time Blow-Up Analysis of Generalized Rosenau-Kawahara-RLW Equations with Caputo Derivatives

Year 2026, Volume: 14 Issue: 1 , 1 - 13 , 30.04.2026

Abdelatif Boutiara , Maamar Benbachır , Jehad Alzabut , Mohammad Esmael Samei

https://izlik.org/JA92HY57KE

Abstract

This paper investigates the  nite-time blow-up of solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation involving the Caputo fractional deriva- tive. By employing the Pohozhaev nonlinear capacity method, we establish sufficient conditions under which the solutions blow up in  nite time. The approach relies on the selection of suitable test functions that satisfy the given initial and boundary conditions. Additionally, we analyze the maximum principle for initial-boundary value problems re- lated to the time-fractional Kawahara equation. Several illustrative examples are pro- vided to validate the theoretical  ndings, and numerical simulations are conducted using MATLAB to support the results. This work contributes to the understanding of blow-up phenomena in nonlinear dispersive wave equations with fractional time derivatives.

Keywords

Rosenau Kawahara RLW Equations , Caputo Derivative , Blow-up Analysis

Project Number

None

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