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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

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Listed:
  • Teng Ren
  • Helu Xiao
  • Zhongbao Zhou
  • Xinguang Zhang
  • Lining Xing
  • Zhongwei Wang
  • Yujun Cui

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.

Suggested Citation

  • Teng Ren & Helu Xiao & Zhongbao Zhou & Xinguang Zhang & Lining Xing & Zhongwei Wang & Yujun Cui, 2019. "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," Complexity, Hindawi, vol. 2019, pages 1-15, September.
    • Handle: RePEc:hin:complx:9278056
    DOI: 10.1155/2019/9278056
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    References listed on IDEAS

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    1. Gao, Lijun & Wang, Dandan & Wang, Gang, 2015. "Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 186-200.
    2. Zhang, Xinguang & Liu, Lishan & Wu, Yonghong & Wiwatanapataphee, B., 2015. "The spectral analysis for a singular fractional differential equation with a signed measure," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 252-263.
    3. Li, Pingrun, 2017. "Generalized convolution-type singular integral equations," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 314-323.
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    Cited by:

    1. Xu Tan & Lining Xing & Zhaoquan Cai & Gaige Wang, 2020. "Analysis of production cycle-time distribution with a big-data approach," Journal of Intelligent Manufacturing, Springer, vol. 31(8), pages 1889-1897, December.
    2. Wang, Guotao & Qin, Jianfang & Zhang, Lihong & Baleanu, Dumitru, 2020. "Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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