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Nonlinear Dynamics

, Volume 71, Issue 4, pp 685–700 | Cite as

Abstract Cauchy problem for fractional differential equations

  • JinRong Wang
  • Yong Zhou
  • Michal Fec̆kan
Original Paper

Abstract

In this paper, a generalized Darbo’s fixed-point theorem associated with Hausdorff measure of noncompactness is established. Then we apply this new variant fixed-point theorem to study some fractional differential equations in Banach spaces via the technique of measure of noncompactness. Many novel existence and uniqueness results for solutions are obtained under the more general conditions.

Keywords

Fractional differential equations Cauchy problems Impulsive problems Nonlocal problems Hausdorff measure of noncompactness 

Notes

Acknowledgements

The first author acknowledges the support by National Natural Science Foundation of China (11201091) and Key Projects of Science and Technology Research in the Chinese Ministry of Education (211169); the second author acknowledges the support by National Natural Science Foundation of China (11271309), Specialized Research Fund for the Doctoral Program of Higher Education (20114301110001) and Key Projects of Hunan Provincial Natural Science Foundation of China (12JJ2001) and the third author acknowledges the support by Grants VEGA-MS 1/0507/11, VEGA-SAV 2/0124/10 and APVV-0414-07.

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of MathematicsGuizhou UniversityGuiyangP.R. China
  2. 2.Department of MathematicsXiangtan UniversityXiangtanP.R. China
  3. 3.Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and InformaticsComenius UniversityBratislavaSlovakia
  4. 4.Mathematical InstituteSlovak Academy of SciencesBratislavaSlovakia

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