Chapter 8 - Controllability of Fractional Higher Order Stochastic Integrodifferential Inclusions

Abstract

A control system is an interconnection of components forming a system configuration which provides a desired system response. Further, controllability is one of the structural properties of dynamical systems and it plays a major role in the development of modern mathematical control theory. Fractional differential and integral equations and inclusions have gained considerable popularity and importance during the past three decades. Moreover, the controllability of fractional dynamical systems is an important issue for many applied problems because the uses of fractional order derivatives and integrals in control theory lead to better results than those of the integer order systems. Also, fractional higher order models of real systems are playing a vital role in control theory and engineering. So in this chapter, a new set of sufficient conditions are derived for controllability of fractional stochastic integrodifferential inclusions of fractional order p∈(0,1] and q∈(1,2] in finite dimensional space by using fractional calculus, fixed point technique, and stochastic analysis approach. In particular, the complete controllability for nonlinear fractional stochastic integrodifferential inclusions is discussed under the proved controllability result of the corresponding linear fractional system.