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Fractional Boundary Value Problems with Integral and Anti-periodic Boundary Conditions

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Abstract

In this paper, we consider a class of boundary value problems of fractional differential equations with integral and anti-periodic boundary conditions, which is a new type of mixed boundary condition. Using the contraction mapping principle, Krasnosel’skii fixed point theorem, and Leray-Schauder degree theory, we obtain some results of existence and uniqueness. Finally, several examples are provided for illustrating the applications of our theoretical analysis.

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Acknowledgments

The author is grateful to the Editor and Referees for their valuable suggestions, which significantly improved the quality of the paper. The author also want to thank Prof. Om P. Agrawal for his helpful discussions. This work was partly supported by the ‘2\(+\)6 Program’ of Central South University and finished during the author was a Postdoc research fellow in School of Mathematics and Statistics.

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Authors and Affiliations

  1. Department of Applied Mathematics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Yufeng Xu

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  1. Yufeng Xu
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Correspondence to Yufeng Xu.

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Communicated by Norhashidah M. Ali.

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Xu, Y. Fractional Boundary Value Problems with Integral and Anti-periodic Boundary Conditions. Bull. Malays. Math. Sci. Soc. 39, 571–587 (2016). https://doi.org/10.1007/s40840-015-0126-0

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  • DOI: https://doi.org/10.1007/s40840-015-0126-0

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