Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions - Chadha, Alka; Sakthivel, Rathinasamy; Bora, Swaroop Nandan Nandan (Nonlinear Analysis: Modelling and Control, 2019)
In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.