An efficient analytical technique for fractional model of vibration equation

The principal purpose of this work is to present an efficient analytical approach based on the q-homotopy analysis transform technique in order to analyze a fractional model of the vibration equation for large membranes. The Laplace decomposition technique is also employed to obtain the solution of the fractional-order vibration equation. Numerical examples are provided to examine the efficiency of the proposed schemes and the results derived are demonstrated graphically. Our examples illustrate that the suggested computational approaches are straightforward to perform and computationally very striking.