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

چکیده مقاله

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. © 2024, University of Nis. All rights reserved.