Abstarct: This thesis focuses on the numerical and semi-analytical solution of the vibration equation for a large membrane, both in its classical and fractional forms. Three main methods are investigated: the modified decomposition method, the homotopy perturbation method, and the operational matrix method baxsed on Legendre Scaling Functions. The modified decomposition method is applied to solve the integer-order equation with rapid convergence, the homotopy perturbation method is used to solve the fractional version with the Caputo derivative, and the operational matrix method transforms the problem into a Sylvester algebraic equation, providing high computational accuracy. The results demonstrate that all three methods are effective, but each involves different trade-offs in terms of accuracy, speed, and computational complexity depending on the specific conditions. Furthermore, the influence of key parameters such as wave speed, time-to-radius ratio, and fractional order on the vibrational response is systematically analyzed.