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

• Published in: Mathematical modelling and analysis Vol. 23; no. 4; pp. 611 - 626
• Main Authors: Wu, Jing, Zhang, Xinguang, Liu, Lishan, Wu, Yonghong, Cui, Yujun
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 09.10.2018
• Subjects: Boundary conditions; Convergence; Convergence (Mathematics); Differential equations; Error analysis; Error analysis (Mathematics); error estimation; fractional p-Laplacian equation; Iteration (Mathematics); Mathematical research; Methods; monotone iterative technique; Stieltjes integral; uniqueness; error estimation; uniqueness; fractional p-Laplacian equation; monotone iterative technique
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2018.037

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.