Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces
Volume 110 / 2014
Annales Polonici Mathematici 110 (2014), 143-169 MSC: Primary 34A37, 34A60; Secondary 35R12, 26A33. DOI: 10.4064/ap110-2-4
We study the existence of mild solutions for a class of impulsive fractional partial neutral integro-differential inclusions with state-dependent delay. We assume that the undelayed part generates an $\alpha $-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by means of the fixed point theorem for discontinuous multi-valued operators due to Dhage and properties of the $\alpha $-resolvent operator. An example is given to illustrate the theory.