Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REGULARITY FOR FRACTIONAL ORDER RETARDED NEUTRAL DIFFERENTIAL EQUATIONS IN HILBERT SPACES

  • Cho, Seong Ho (Department of Applied Mathematics Pukyong National University) ;
  • Jeong, Jin-Mun (Department of Applied Mathematics Pukyong National University) ;
  • Kang, Yong Han (Institute of Liberal Education Catholic University of Daegu)
  • Received : 2015.06.15
  • Published : 2016.09.01
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Abstract

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

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Acknowledgement

Supported by : National Foundation of Korea(NRF)

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