Journal
APPLICABLE ANALYSIS
Volume 94, Issue 6, Pages 1235-1258Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00036811.2014.924214
Keywords
26A33; 93B05; 60H15; 34K05; -resolvent operator; approximate controllability; infinite delay; multi-valued map; fractional stochastic neutral integro-differential inclusions
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In this paper, the approximate controllability of a class of fractional stochastic neutral integro-differential inclusions with infinite delay in Hilbert spaces is considered. By using the Holder inequality, the -resolvent operator and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear fractional stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the proposed theory.
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