<p>This work focuses on the controllability problems of Hilfer fractional backward evolution equations. Firstly, existence and uniqueness results are displayed by employing the iteration sequence approach. Then, the approximate controllability problem is explored by iteration and approximation sequence techniques involving resolvent and integral contractor. Additionally, with the aid of suitable conditions, by Banach’s fixed point theorem, the exact null controllability result is exhibited without involving the inverse of the control operator. The idea can also be well adapted to the exact controllability problem. Moreover, an important example is supplied to manifest the feasibility of our findings. Eventually, the conclusion of this work is offered.</p>

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Controllability of Hilfer fractional backward evolution systems

  • Shouguo Zhu

摘要

This work focuses on the controllability problems of Hilfer fractional backward evolution equations. Firstly, existence and uniqueness results are displayed by employing the iteration sequence approach. Then, the approximate controllability problem is explored by iteration and approximation sequence techniques involving resolvent and integral contractor. Additionally, with the aid of suitable conditions, by Banach’s fixed point theorem, the exact null controllability result is exhibited without involving the inverse of the control operator. The idea can also be well adapted to the exact controllability problem. Moreover, an important example is supplied to manifest the feasibility of our findings. Eventually, the conclusion of this work is offered.