Mamadu Variational Iteration Method for the Solution of Time-Fractional Telegraph Equation

In this paper, the Mamadu Variational Iteration Method (MVIM) is developed as a powerful numerical toolbox for obtaining analytical and approximate solutions to the time-fractional telegraph equation. The method involves constructing an iterative correction functional that incorporates Caputo fractional derivatives and Mamadu weighting, ensuring rapid convergence and improved accuracy compared to the classical Variational Iteration Method (VIM). Numerical results confirm the effectiveness of MVIM in resolving time-fractional telegraph equations with high accuracy and computational efficiency. By introducing the MVIM mathematical framework, the present method contributes to the ongoing advancement of analytical methods for solving fractional partial differential equations and expands the subject area to researchers and practitioners in mathematical modeling, engineering, and physics.