Solving Multidimensional Fractional Telegraph Equation by Using Yang Hussein Jassim method

This study employs the Young Hussein Jassim (YHJ)technique to examine the exact solutions of the space-time telegraphequation analytically (ST-TE). The YHJ approach is an innovative andappealing hybrid transformation integration method, effectivelycombining the HJ and Young methods. Through a simplified iterativeprocess with minimal computational requirements, this approach quicklyprovides convergent, sequential solutions. The reliability of the methodis demonstrated by applying it to two case studies of the ST-TE withinthe framework of the Tania derivative, which includes the definition ofnon-singular kernel functions. The study also includes extensivecomparisons between approximate, exact, and relevant literature-basedsolutions to assess the technique's accuracy andeffectiveness. Graphical representations illustrate the effect ofnon-integer temporal and spatial parameters on solution behavior. Thefindings suggest that this method is easy to implement and suitable forexploring complex physical models governed by nonlinear partialdifferential equations with fractional time components.