Electron. J. Diff. Equ., Vol. 2013 (2013), No. 81, pp. 1-21.

Existence of solutions to impulsive fractional partial neutral stochastic integro-differential inclusions with state-dependent delay

Zuomao Yan, Hongwu Zhang

Abstract:
We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O'Regan and properties of the solution operator. An example is given to illustrate the theory.

Submitted September 25, 2012. Published March 29, 2013.
Math Subject Classifications: 34A37, 60H10, 34K50, 34G25, 26A33.
Key Words: Impulsive stochastic integro-differential inclusions; state-dependent delay; multi-valued map; fractional neutral integro-differential inclusions.

Show me the PDF file (300 KB), TEX file for this article.

Zuomao Yan
Department of Mathematics, Hexi University
Zhangye, Gansu 734000, China
email: yanzuomao@163.com
Hongwu Zhang
Department of Mathematics, Hexi University
Zhangye, Gansu 734000, China
email: zh-hongwu@163.com

Return to the EJDE web page