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Well-posedness of a kind of nonlinear coupled system of fractional differential equations

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Abstract

We study the boundary value problem of a coupled differential system of fractional order, and prove the existence and uniqueness of solutions to the considered problem. The underlying differential system is featured by a fractional differential operator, which is defined in the Riemann-Liouville sense, and a nonlinear term in which different solution components are coupled. The analysis is based on the reduction of the given system to an equivalent system of integral equations. By means of the nonlinear alternative of Leray-Schauder, the existence of solutions of the factional differential system is obtained. The uniqueness is established by using the Banach contraction principle.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    XiaoJun Zhou & ChuanJu Xu

  2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang, 550001, China

    XiaoJun Zhou

Authors
  1. XiaoJun Zhou
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  2. ChuanJu Xu
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Correspondence to ChuanJu Xu.

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Zhou, X., Xu, C. Well-posedness of a kind of nonlinear coupled system of fractional differential equations. Sci. China Math. 59, 1209–1220 (2016). https://doi.org/10.1007/s11425-015-5113-2

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  • DOI: https://doi.org/10.1007/s11425-015-5113-2

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