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The spectral analysis for a singular fractional differential equation with a signed measure

Author

Listed:
  • Zhang, Xinguang
  • Liu, Lishan
  • Wu, Yonghong
  • Wiwatanapataphee, B.

Abstract

In this paper, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, we obtain some properties of the first eigenvalue of a fractional differential equation. Based on these properties, the fixed point index of the nonlinear operator is calculated explicitly and some sufficient conditions for the existence of positive solutions are established.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:257:y:2015:i:c:p:252-263
    DOI: 10.1016/j.amc.2014.12.068
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    References listed on IDEAS

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    1. Jing Wu & Xinguang Zhang, 2012. "Eigenvalue Problem of Nonlinear Semipositone Higher Order Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Xinguang Zhang & Lishan Liu & Benchawan Wiwatanapataphee & Yonghong Wu, 2012. "Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Fang Wang & Lishan Liu & Yonghong Wu & Yumei Zou, 2019. "Iterative Analysis of the Unique Positive Solution for a Class of Singular Nonlinear Boundary Value Problems Involving Two Types of Fractional Derivatives with p -Laplacian Operator," Complexity, Hindawi, vol. 2019, pages 1-21, October.
    3. Yongyi Gu & Fanning Meng, 2019. "Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods," Complexity, Hindawi, vol. 2019, pages 1-11, August.
    4. Yang Yang & Jian-ming Qi & Xue-hua Tang & Yong-yi Gu, 2019. "Further Results about Traveling Wave Exact Solutions of the (2+1)‐Dimensional Modified KdV Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    5. 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.

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