Optimality of fractional impulsive partial stochastic differential systems with analytic sectorial operators and controls

Abstract

In this paper, we study a class of fractional impulsive partial stochastic differential systems with analytic sectorial operators and not instantaneous impulses in separable Hilbert spaces. Firstly, the existence of mild solutions and optimal mild solutions investigated by utilizing the theory of analytic sectorial operators, stochastic analysis, suitable fixed point theorems with the Hausdorff measure of noncompactness. Secondly, the question of exact controllability of these control systems is considered too. Finally, an example to illustrate the applications of main results is also given.

Keywords:

• Fractional impulsive partial stochastic differential systems
• optimality
• exact controllability
• Hausdorff measure of noncompactness
• fixed point theorem

2010 MR Subject Classifications:

• 34A37
• 60H15
• 26A33
• 93B05

Acknowledgements

The authors would like to thank the editor and the reviewers for their constructive comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (11461019), the President Fund of Scientific Research Innovation and Application of Hexi University (xz2013-10).