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Existence results for boundary value problems of high order differential equations involving Caputo derivative

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Abstract

We study boundary value problems for differential equations involving Caputo derivative of order α∈(n−1,n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Hölder’s inequality, a suitable singular Gronwall’s inequality and fixed point theorem via a priori estimate method. At last, three examples are given to illustrate the results.

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Authors and Affiliations

  1. College of Technology of Guizhou University, Guiyang, Guizhou, 550004, P.R. China

    YanLong Yang

  2. Department of Mathematics, Guizhou University, Guiyang, Guizhou, 550025, P.R. China

    Linli Lv & JinRong Wang

Authors
  1. YanLong Yang
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  2. Linli Lv
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  3. JinRong Wang
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Correspondence to JinRong Wang.

Additional information

The first author acknowledge support from the Youth Teachers Natural Science Foundation of Guizhou University (2009, No. 083). The second and third authors acknowledge support from Tianyuan Special Funds of the National Natural Science Foundation of China (11026102).

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Yang, Y., Lv, L. & Wang, J. Existence results for boundary value problems of high order differential equations involving Caputo derivative. J. Appl. Math. Comput. 38, 565–583 (2012). https://doi.org/10.1007/s12190-011-0497-9

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  • DOI: https://doi.org/10.1007/s12190-011-0497-9

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