A Chebyshev pseudo-spectral method for solving numerically linear and nonlinear fractional-order integro-differential equations of Volterra type is considered. The fractional derivative is described in the Caputo sense. The suggested method reduces these types of equations to the solution of linear or nonlinear algebraic equations. Special attention is given to study the convergence of the proposed method. Finally, some numerical examples are provided to show that this method is computationally efficient, and a comparison is made with existing results.

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet with a power-law surface velocity, slip velocity, and variable thickness. The flow is caused by nonlinear stretching of the sheet. The governing partial differential equations are transformed into a nonlinear ordinary differential equation with appropriate boundary conditions for various physical parameters. The remaining ordinary differential equation is solved numerically by using the Chebyshev spectral method. The effects of the slip parameter and the wall thickness parameter on the flow profile and local skin friction are presented. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted.