Spectral treatment for the fractional-order wave equation using shifted Chebyshev orthogonal polynomials

This paper will examine the approximate solution for the fractional-order wave equation. The method used for this purpose fundamentally is based on the second kind of Chebyshev polynomials besides the Chebyshev collocation mechanism in addition to the forward finite difference scheme. The fractional-order terms are expressed through Caputo's fractional-order derivative definition. With these tools, the problem will be converted into an algebraic system of equations that are solved numerically. The accuracy and applicability of the proposed technique are demonstrated through some given numerical applications.