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http://dx.doi.org/10.4134/JKMS.j150354

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)
Publication Information
Journal of the Korean Mathematical Society / v.53, no.5, 2016 , pp. 1019-1036 More about this Journal
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.
Keywords
fractional differential equation; retarded system; regularity; analytic semigroup; fractional power;
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