Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 81, pp. 1-21.
Title: Existence of solutions to impulsive fractional partial neutral
stochastic integro-differential inclusions with state-dependent delay
Authors: Zuomao Yan (Hexi Univ., Zhangye, Gansu, China)
Hongwu Zhang (Hexi Univ., Zhangye, Gansu, China)
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.