Iterative refinement for a system of linear integro-differential equations of fractional type

A novel technique based on iterative refinement is developed to approximate the analytical solution of a system of linear fractional integro-differential equations. While the study focuses mainly on Fredholm-type equations, adaptation to the Volterra-type is also presented. A comparison is made with the method of successive approximations on the basis of convergence speed and accuracy. Several numerical examples are given to demonstrate the efficacy of our algorithm. The authors also present formulations of some error bounds.