Controllability of Impulsive Damped Fractional Order Systems Involving State Dependent Delay (Contemporary Mathematics, 2024)
In this article, the concept of controllability on fractional order impulsive systems involving state dependent delay and damping behavior is analysed by utilizing Caputo fractional derivative. The main motivation is to derive the sufficient conditions for the controllability of the considered systems. Based on the Laplace transform and inverse Laplace transform, the solution of fractional-order dynamical systems are obtained. The results are established by utilizing basic ideas of fractional calculus, Mittag-Leffler function and Banach fixed point theorem. Finally, an application is provided to illustrate the derived result.
Keywords: fractional damped system; impulsive system; state dependent delay; fixed point theorem; controllability