Fixed-point theory and Green’s functions for the solution of DEs: An iterative strategy

Abstract

A recently developed iterative method for estimating the solution of ordinary and fractional boundary-value problems is described. The strategy is based on the construction of a tailored integral operator described in terms of the Green's function, which corresponds to the highest order linear derivative term. After then, the integral operator is subjected to a fixed-point scheme like Picard's, Mann's, or Ishikawa's. The convergence of the scheme is assessed. Numerical tests are used to assess the applicability and correctness of the approach.