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Existence results for fractional semilinear differential inclusions in Banach spaces

  • Xiaoyou Liu
  • Zhenhai Liu
Applied mathematics

Abstract

We consider the existence of mild solutions for fractional semilinear differential inclusions involving a nonconvex set-valued map in Banach spaces. First, we study the continuous property of the solution map for an auxiliary fractional differential equation. Then the main result is obtained by using this solution map, selection theorems from multivalued analysis and Schauder’s fixed point theorem. Finally an example to illustrate the applications of the main result is also given.

Keywords

Fractional semilinear differential inclusion Mild solution Nonconvex multifunction 

Mathematics Subject Classification (2010)

34G20 26A33 93C25 

Notes

Acknowledgements

The authors are grateful to anonymous referees for their constructive comments and suggestions which led to improvement of the original manuscript.

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Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

  1. 1.School of Mathematical Science and Computing TechnologyCentral South UniversityChangshaP.R. China
  2. 2.School of ScienceGuangxi University for NationalitiesNanningP.R. China

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