Controllability of non‐autonomous fractional delay control system of order ϱ∈(1,2]

This paper investigates the exact controllability of a class of non‐autonomous fractional delay control systems involving Caputo derivatives of order . The system is considered under nonlocal initial conditions. To address the exact controllability problem, we employ the framework of fractional evolution families along with Krasnoselskii's fixed point theorem(FPT). This approach establishes the sufficient conditions to ensure the existence of a control that drives the system to the desired final state. The applicability and efficacy of the proposed theoretical results are validated with the help of examples.