Abstract
The two approaches to solving nonlinear Caputo time-fractional wave-like equations with variable coefficients are examined in this study. The Homotopy perturbation transform method and the Yang transform decomposition method are the names of these two techniques. Three separate numerical examples are provided to demonstrate the effectiveness and precision of the suggested methods. The results were acquired to demonstrate the effectiveness and power of the two approaches, providing estimates with better precision and closed form solutions. The solutions to these kinds of equations can be found using the suggested methods as infinite series, and when these series are in closed form, they provide the exact solution. The suggested techniques have been demonstrated to be effective and efficient in their application. Three numerical examples are used to examine the methods accuracy and effectiveness.