Rajarama Mohan Jena - National Institute of Technology Rourkela, Department of Mathematics, Odisha, Rourkela, ۷۶۹۰۰۸, India
S. Chakraverty - National Institute of Technology Rourkela, Department of Mathematics, Odisha, Rourkela, ۷۶۹۰۰۸, India

The primary aim of this manuscript is to present the approximate analytical solutions of the time fractional order α (1<α≤2) Vibration Equation (VE) of large membranes with the use of an iterative technique namely Residual Power Series Method (RPSM). The fractional derivative is defined in the Caputo sense. Example problems have been solved to demonstrate the efficacy of the present method and the results obtained are verified graphically. The convergence analysis of the proposed method has also been included in this article. It is seen that the present method is found to be reliable, very effective and easy to implement for various kinds of fractional differential equations used in science and engineering.

Fractional vibration equation, Caputo derivative, Residual Power Series, Mittag-Leffler function