On a new class of impulsive stochastic partial neutral integro-differential equations

Abstract

In this paper, we introduce a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and not instantaneous impulses in separable Hilbert spaces. We prove the existence of mild solutions for these equations in the -norm without the assumptions of compactness. The results are obtained using suitable fixed point theorems with the properties of analytic resolvent operators. Finally, an example is presented to illustrate the theory.

Keywords:

• impulsive stochastic partial neutral functional integro-differential equations
• infinite delay
• analytic resolvent operators
• fractional power
• fixed point theorem

AMS Subject Classifications:

• 34A37
• 34A60
• 34K40
• 60H15

Acknowledgements

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

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11461019]; The President Found of Scientific Research Innovation and Application of Hexi University [grant number xz2013-10].