Abstract
In this paper, the approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in a Hilbert space is studied. By using the nonlinear alternative of Leray-Schauder type for multivalued maps due to O’Regan and properties of the α-resolvent operator combined with approximation techniques, we derive a new set of sufficient conditions for the approximate controllability of fractional impulsive evolution system under the assumption that the corresponding linear system is approximately controllable. An example is provided to illustrate the obtained theory.
Highlights
1 Introduction The study of impulsive functional differential equations is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution
The nonlinear fractional differential equations has in recent years been an object of increasing interest because of its wide applicability in nonlinear oscillations of earthquakes, and many physical phenomena such as seepage flow in porous media and in fluid dynamic traffic models; see [ – ]
The existence of solutions for fractional semilinear differential or integrodifferential equations has been extensively studied by many authors [ – ]
Summary
The study of impulsive functional differential equations is linked to their utility in simulating processes and phenomena subject to short-time perturbations during their evolution. Many authors [ – ] were interested in the existence of solutions for fractional functional differential equations with infinite delay in Banach spaces.
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