A new approach on the approximate controllability of fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces

This manuscript is mainly focusing on approximate controllability for fractional differential evolution equations of order 1 < r < 2 in Hilbert spaces. We consider a class of control systems governed by the fractional differential evolution equations. By using the results on fractional calculus, cosine and sine functions of operators, and Schauder's fixed point theorem, a new set of sufficient conditions are formulated which guarantees the approximate controllability of fractional differential evolution systems. The results are established under the assumption that the associated linear system is approximately controllable. Then, we develop our conclusions to the ideas of nonlocal conditions. Lastly, we present theoretical and practical applications to support the validity of the study. (C) 2020 Elsevier Ltd. All rights reserved.