CONTROLLABILITY OF THE TIME-VARYING FRACTIONAL DYNAMICAL SYSTEMS HAVING MULTIPLE DELYAS IN CONTROL WITH CAPUTO FRACTIONAL DERIVATIVE

The objective of this study is to analyze controllability results for time-varying linear and nonlinear fractional dynamical systems with multiple control delays within the framework of the Caputo fractional derivative. This paper focuses on examining control problems within a finite time interval, aiming to identify a control function that steers the system’s solution from a specified initial state to a targeted final state. For linear systems, the study establishes necessary and sufficient conditions for controllability by utilizing the Grammian matrix techniques. For nonlinear systems, the existence of a solution is ensured through an iterative technique, with completeness of the space guaranteed. With the help of this technique, we establish the sufficient conditions for the controllability of time-varying nonlinear fractional dynamical systems. The results show that the controllability of fractional dynamical systems can be effectively analyzed with the given framework, along with numerical simulations and graphical representations to clarify the theoretical findings.