Innovation of Yang Hussein Jassim’s method in solving nonlinear telegraph equations across multiple dimensions

This research utilizes the Yang Hussein Jassim method (YHJM) approach to investigate the precise solutions of the space–time telegraph equation analytically (ST-TE). The Yang Hussein Jassim method (YHJM) approach is an innovative and appealing hybrid transformation integration method, effectively combining the Hussein Jassim (HJM) and Yang transform (Ya). Through a simplified iterative process with minimal computational requirements, this approach quickly provides convergent, sequential solutions. The reliability of the method is demonstrated by applying it to two case studies of the ST-TE within the framework of the Tania derivative, which includes the definition of non-singular kernel functions. The study also includes extensive comparisons between approximate, exact, and relevant literature-based solutions to assess the technique’s accuracy and effectiveness. Visual depictions demonstrate the influence of fractional temporal and spatial parameters on the behavior of solutions. The results indicate that this approach is straightforward to apply and effective for analyzing intricate physical models described by nonlinear partial differential equations with fractional time terms.