Abstract
We discuss the approximate controllability of nonlinear fractional integro-differential system under the assumptions that the corresponding linear system is approximately controllable. Using the fixed-point technique, fractional calculus and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional integro-differential equations are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.
Highlights
Controllability is one of the fundamental concepts in mathematical control theory, which plays an important role in control systems
The controllability of nonlinear systems represented by evolution equations or inclusions in abstract spaces and qualitative theory of fractional differential equations has been extensively studied by several authors
A pioneering work on the approximate controllability of deterministic and stochastic systems has been reported by Bashirov and Mahmudov [ ], Dauer and Mahmudov [ ] and Mahmudov [ ]
Summary
Controllability is one of the fundamental concepts in mathematical control theory, which plays an important role in control systems. The approximate controllability for various kinds of (fractional) differential equations has generated considerable interest. There exists only a limited number of papers on the approximate controllability of the fractional nonlinear evolution systems.
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