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Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions

Author

Listed:
  • Wang, Guotao
  • Qin, Jianfang
  • Zhang, Lihong
  • Baleanu, Dumitru

Abstract

By using the monotone iterative method combined with the upper and lower solutions, we not only prove the existence of extremal solutions for the nonlinear fractional Langevin equation involving fractional conformable derivative and non-separated integro-differential strip-multi-point boundary conditions, but also provide two computable explicit monotone iterative sequences that converge to the extremal solution. In order to carry out our work smoothly, we also develop a comparison principle, which plays a very important role in this article.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304229
    DOI: 10.1016/j.chaos.2019.109476
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    References listed on IDEAS

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    1. Pei, Ke & Wang, Guotao & Sun, Yanyan, 2017. "Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain," Applied Mathematics and Computation, Elsevier, vol. 312(C), pages 158-168.
    2. 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.
    3. Yong-Kui Chang & Yatian Pei & Rodrigo Ponce, 2019. "Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type Via Fractional Resolvent Operators," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 558-572, August.
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