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

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Authors
Wu, J.
Zhang, Xinguang
Liu, Lishan
Wu, Yong Hong
Cui, Y.
Date
2018
Type
Journal Article

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Wu, J. and Zhang, X. and Liu, L. and Wu, Y.H. and 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): pp. 611-626.
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Mathematical Modelling and Analysis
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School of Electrical Engineering, Computing and Mathematical Science (EECMS)
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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.