konuralp j. math. Konuralp Journal of Mathematics 2147-625X Mehmet Zeki SARIKAYA Biological Mathematics Dynamical Systems in Applications Biyolojik Matematik Uygulamalarda Dinamik Sistemler Finite-Time Blow-Up Analysis of Generalized Rosenau-Kawahara-RLW Equations with Caputo Derivatives Boutiara Abdelatif University of Ghardaia https://orcid.org/0000-0003-3519-1153 Benbachır Maamar Saad Dhab University https://orcid.org/0000-0002-5262-1138 Alzabut Jehad Prince Sultan University/Ostim Technical University Samei Mohammad Esmael Bu Ali Sina 04 30 2026 14 1 1 13 11 24 2025 04 27 2026 Copyright © 2013, Konuralp Journal of Mathematics 2013 Konuralp Journal of Mathematics

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.

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