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Eigenvalue problems for fractional differential equations with right and left fractional derivatives

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  • Li, Jing
  • Qi, Jiangang

Abstract

This paper studies the eigenvalue problem of a class of fractional differential equations with right and left fractional derivatives. With the aid of the spectral theory of compact self-adjoint operators in Hilbert spaces, we show that the spectrum of this problem consists of only countable real eigenvalues with finite multiplicity and the corresponding eigenfunctions form a complete orthogonal system. Furthermore, the lower bound of the eigenvalues is obtained.

Suggested Citation

  • Li, Jing & Qi, Jiangang, 2015. "Eigenvalue problems for fractional differential equations with right and left fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 1-10.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:1-10
    DOI: 10.1016/j.amc.2014.12.146
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    References listed on IDEAS

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    1. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
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