Approximate controllability results for non-densely defined fractional neutral differential inclusions with Hille–Yosida operators

ABSTRACT

In this paper, we mainly focused the approximate controllability results for a class of non-densely defined fractional neutral differential control systems. First, we establish a set of sufficient conditions for the approximate controllability for a class of fractional differential inclusions with infinite delay where the linear part is non-densely defined and satisfies the Hille–Yosida condition. The main techniques rely on Bohnenblust– Karlin's fixed point theorem, operator semigroups and fractional calculus. Further, we extend the result to study the approximate controllability concept with nonlocal conditions. Finally, an example is also given for the illustration of the obtained theoretical results.

KEYWORDS:

• Approximate controllability
• fractional differential inclusions
• integrated semigroup
• Hille–Yosida condition
• multivalued map
• integral solution
• nonlocal conditions

SUBJECT CLASSIFICATION CODES:

• 34A08
• 34G20
• 34K40
• 34G20
• 47H10

Acknowledgments

The authors are deeply grateful to the anonymous referees for the careful reading of this paper and helpful comments, which have been very useful for improving the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.