A numerical iterative approach for solving weakly singular Volterra fractional integral equations

Abstract

This paper explores a new numerical iterative approach for approximating solutions of fractional Volterra integral equations, based on the successive approximations method and the product integration method. Under certain conditions, we prove the existence and uniqueness of the solution and give error estimates of the approximations. Furthermore, both of the convergence analysis and numerical stability of the suggested method are examined. In the end, some examples confirm the theoretical results and illustrate the accuracy of the approach.