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

    Xinguang Zhang Affiliation
    ; Jing Wu Affiliation
    ; Lishan Liu Affiliation
    ; Yonghong Wu Affiliation
    ; Yujun Cui Affiliation

Abstract

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.

Keyword : uniqueness, fractional p-Laplacian equation, monotone iterative technique, error estimation

How to Cite
Zhang, X., Wu, J., Liu, L., Wu, Y., & Cui, Y. (2018). Convergence analysis of iterative scheme and error estimation of positive solution for a fractional differential equation. Mathematical Modelling and Analysis, 23(4), 611-626. https://doi.org/10.3846/mma.2018.037
Published in Issue
Oct 9, 2018
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