CONTROLLABILITY OF NON-LINEAR FRACTIONAL-ORDER SYSTEMS WITH DAMPING BEHAVIOUR AND MULTIPLE DELAYS

Abstract

A controllability analysis of both linear and non-linear fractional-order systems with damping behaviour and multiple delays is studied. We derived the controllability result for damped system with multi-term fractional order and multiple delays by introducing some lemmas with the help of Laplace transform properties and Mittag–Leffler function. Further, some new sufficient conditions ensuring controllability for a class of non-linear multi-term fractional-order damped systems with multiple delays are established by utilizing fractional Caputo derivatives and Schauder’s fixed point theorem. Moreover, as applications that demonstrate the proposed results, two examples are presented.