Approximate controllability of a fractional stochastic partial integro-differential systems via noncompact operators. Issue 4 (4th July 2019)

• Record Type: Journal Article
• Authors: Yan, Zuomao; Han, Li
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 4(2019)
• Page Start: 636
• Page End: 667
• Publication Date: 2019-07-04
• Subjects: Approximate controllability -- fractional impulsive stochastic partial integro-differential systems -- measure of noncompactness -- fractional resolvent operators -- fixed point; 34A37 -- 60H15 -- 34K50 -- 26A33 -- 93B05; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1605910
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: Objective: in this article, we discuss the approximate controllability problems of a new class of fractional impulsive stochastic partial integro-differential systems in separable Hilbert spaces. Methods: by applying the fractional calculus, the measure of noncompactness, properties of fractional resolvent operators and fixed point theorems. Results: we prove our main results without the hypotheses of compactness on the operator generated by the linear part of systems. Instead we suppose that the nonlinear term only satisfies a weakly compactness condition. Conclusion: the approximate controllability for the control systems with noncompact operators is established. Finally, an example is given for the illustration of the obtained theoretical results.