Convergence analysis of iterative scheme and error estimation of positive solution for a fractional differential equation

Abstract

© 2018 The Author(s). In this paper, we focus on the iterative scheme and error estimation of positive solutions for a class of p-Laplacian fractional order differential equation subject to Riemann-Stieltjes integral boundary condition. Under a weaker growth condition of nonlinearity, by using a monotone iterative technique, we first establish a new result on the sufficient condition for the existence of a unique positive solution to the above problem, then construct an iterative scheme which converges to the unique positive solution, and then present an error estimation and the exact convergence rate of the approximate solution.