A novel approach to solving nonlinear fractional wave-like differential equations

Abstract

The optimal auxiliary function method (OAFM) is applied in this research paper to find analytical solutions to fractional-order strongly nonlinear wave-like differential equations with variable coefficients. This is a revolutionary semi-numerical technique for solving complex nonlinear partial differential equations (PDEs) in a broad spectrum of applications. For validation of the recommended method, we apply it to two nonlinear time-fractional wave-like equations (NTFWLs). The technique’s effectiveness and applications are shown through mathematical and graphical analysis of the consequences obtained; also, it is further investigated to determine how partial arrangement affects the behavior of the obtained results. The obtained results suggest that the methods used are operative and effective at resolving fractional evolution problems and other fractional models that arise in nonlinear techniques. © 2026 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the University of Bahrain.