Application of homotopy perturbation method and homotopy analysis method to fractional vibration equation

In this paper, the approximate analytical solutions of the mathematical model of vibration equation with fractional-order time derivative β (1<β≤2) for very large membranes are obtained with the help of powerful mathematical tools like homotopy perturbation method and homotopy analysis method. Both the methods perform extremely well in terms of efficiency and simplicity. The validity and applicability of the techniques are shown for obtaining approximate numerical solutions for different particular cases which are presented through figures and tables.