Variational Approach to Finite-Approximate Controllability of Sobolev-Type Fractional Systems - Mahmudov, Nazim, I (Springer/Plenum Publishers, 2020)
In this work, we extend a variational approach to study the finite-approximate controllability for Sobolev-type fractional semilinear evolution equations with nonlocal conditions in Hilbert spaces. Assuming the approximate controllability of the corresponding linear equation, we obtain sufficient conditions for the finite-approximate controllability of the Sobolev-type fractional system. We prove that, with one sole control, one can obtain simultaneously approximate controllability and exact reachability of a finite number of constraints. The obtained result is a generalization and continuation of the recent results on this issue. An example is given as an application of our result.
Keywords: Finite-approximate controllability; Fractional evolution systems; Nonlocal conditions; Gramian controllability operator; Mittag-Leffler functions