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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.

Controllability of impulsive semilinear functional differential inclusions with finite delay in Fréchet spaces

Abada Nadjat;  Benchohra Mouffak;  Hammouche Hadda;  Ouahab Abdelghani — 2007

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we use the extrapolation method combined with a recent nonlinear alternative of Leray-Schauder type for multivalued admissible contractions in Fréchet spaces to study the existence of a mild solution for a class of first order semilinear impulsive functional differential inclusions with finite delay, and with operator of nondense domain in original space.

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