The Iterative Scheme and the Convergence Analysis of Unique Solution for a Singular Fractional Differential Equation from the Eco-Economic Complex System's Co-Evolution Process. (2nd September 2019)

• Record Type: Journal Article
• Authors: Ren, Teng; Xiao, Helu; Zhou, Zhongbao; Zhang, Xinguang; Xing, Lining; Wang, Zhongwei; Cui, Yujun
• Other Names: Kuniya Toshikazu Academic Editor.
• Is Part Of: Complexity. Volume 2019(2019)
• Publication Date: 2019-09-02
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2019/9278056
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : In this paper, we focus on a class of singular fractional differential equation, which arises from many complex processes such as the phenomenon and diffusion interaction of the ecological-economic-social complex system. By means of the iterative technique, the uniqueness and nonexistence results of positive solutions are established under the condition concerning the spectral radius of the relevant linear operator. In addition, the iterative scheme that converges to the unique solution is constructed without request of any monotonicity, and the convergence analysis and error estimate of unique solution are obtained. The numerical example and simulation are also given to demonstrate the application of the main results and the effectiveness of iterative process.