In this study, the collocation method and first-kind Chebyshev polynomials are used to investigate the solution of fractional integral-differential equations. In order to solve the problem, we first convert it to a set of linear algebraic equations, which are then solved by using matrix inversion to get the unknown constants. To demonstrate the theoretical findings, a few numerical examples are given and compared with other results obtained by other numerical techniques. Tables and figures are utilized to demonstrate the accuracy and effectiveness of the method. The outcomes demonstrate that the method improved accuracy more effectively while requiring less labor-intensive tasks.