Operational matrix ‎approach ‎‎for solving ‎fractional vibration equation of large ‎membranes ‎‎with error estimation

Abstract

The principal purpose of this work is to ‎present ‎a‎ numerical technique for the fractional vibration equation of large ‎membranes.‎ This method uses the Chebyshev cardinal functions ‎and ‎the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix ‎o‎f derivative, the time fractional vibration ‎equation‎ is reduced to a set of algebraic equations. ‎Mea‎nwhile‎, an estimation of the error bound for this algorithm ‎is ‎given‎ on the basis ‎of‎ some ‎theorems. ‎‎‎‎‎‎‎Two‎ numerical examples are included ‎by ‎taking‎ different initial conditions ‎to demonstrate the efficiency and applicability of ‎this ‎approach‎. ‎‎T‎o examine ‎the ‎‎accuracy ‎of the ‎suggested ‎method, ‎the ‎n‎umerical results are compared with the existing analytical ‎methods.‎