Numrical Solutions of Multi-Dimensional Fractional Telegraph Equations

Abstract

This study employs the *Young Variational Iteration  Method (YVIM)* to analyze the analytical solutions of the spatio-temporal Telegraph equation (ST-TE). *YVIM* is an innovative and attractive hybrid integral transformation strategy that elegantly combines *VIM* and *Young* transformation methods. This solution strategy effectively and rapidly generates convergent series-type solutions through an iterative process that requires fewer computations. The method’s validity is demonstrated by applying it to two test cases (ST-TE) within the framework of *Tanya’s derivative*, which includes the definition of non-singular kernel functions. The study includes numerous comparisons between the approximate solutions, exact solutions, and those available in the relevant literature to verify the accuracy and effectiveness of the technique. Graphical representations are provided to illustrate the impact of incorrect, temporal, and spatial parameters on the behavior of the obtained solutions. The results suggest that the method is straightforward to implement and can be used to explore complex physical systems governed by nonlinear partial differential equations with fractional time components.