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- Title
Optimal Controls for Fractional Stochastic Functional Differential Equations of Order α∈(1,2].
- Authors
Yan, Zuomao; Jia, Xiumei
- Abstract
In this paper, we study optimal control problems for a class of fractional stochastic functional differential equations of order α∈(1,2]<inline-graphic></inline-graphic> in Hilbert spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence of mild solutions are investigated by using the fractional calculus, stochastic analysis theory, and fixed point theorems with the strongly continuous α<inline-graphic></inline-graphic>-order cosine family. Then, the existence conditions of optimal pairs of systems governed by a fractional stochastic partial differential equations of order α∈(1,2]<inline-graphic></inline-graphic> with infinite delay are presented. The results are obtained under the mixed Lipschitz and Carathéodory conditions. Finally, an example is presented to illustrate the main results.
- Subjects
STOCHASTIC differential equations; OPTIMAL control theory; HILBERT space; FRACTIONAL calculus; STOCHASTIC analysis
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2018, Vol 41, Issue 3, p1581
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-016-0415-2