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Existence of solutions for impulsive fractional partial neutral integro-differential inclusions with state-dependent delay in Banach spaces

Zuomao Yan, Hongwu Zhang (2014)

Annales Polonici Mathematici

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 α-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 α-resolvent operator. An example is given to illustrate the...

Existence results for delay second order differential inclusions

Dalila Azzam-Laouir, Tahar Haddad (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, some fixed point principle is applied to prove the existence of solutions for delay second order differential inclusions with three-point boundary conditions in the context of a separable Banach space. A topological property of the solutions set is also established.

Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

Hammouche Hadda, Guerbati Kaddour, Benchohra Mouffak, Abada Nadjat (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.

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