Note on "An existence result with numerical solution of nonlinear fractional integral equations"

Abstract

The recent iterative numerical method in [Kazemi, Manochehr, Amar Deep, and Juan Nieto, "An existence result with numerical solution of nonlinear fractional integral equations," Mathematical Methods in the Applied Sciences ( 2023)] requires some corrections, as we point out in this note. We give a counterexample to one of their main statements (Theorem 5.1). The iterative method used is untrue, and we will correct it.With an example, it can be seen that using the midpoint rule will not be suitable and accurate in fractional cases (0 < τ < 1); instead, using Jacobi's quadrature rule can work well. Also, to show the validity of our numerical method, a non-linear example is considered.MSC: 60H20, 47H10.