Approximate controllability of fractional stochastic differential inclusions with nonlocal conditions

Abstract

In this paper, we investigate the approximate controllability of fractional stochastic differential inclusions with nonlocal conditions. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear fractional stochastic differential inclusions under the assumption that the corresponding linear system is approximately controllable. In addition, we establish the approximate controllability results for the fractional stochastic control system with infinite delay. The results are obtained with the help of the fixed-point theorem for multivalued operators and fractional calculus. Also, two examples are provided to illustrate the obtained theory. ARTICLE HISTORY

Approximate Controllability of Impulsive Stochastic Fractional Differential Equations With Nonlocal Conditions

“…The ap-proximate controllability is the weaker concept of controllability receiving much attention. In this case it is possible to steer the system to an arbitrary small neighborhood of the final state [17,18,20,21,24,32,33,35,50,51]. However, stochastic control theory which is a generalization of classical control theory has rarely been reported.…”

“…The biggest difficulty is the analysis of a stochastic control system and stochastic calculations induced by the stochastic process. For more details, see [14,16,19,23,34,36,39,50,52].…”

“…For more details, see [15,19,22,29,39,43,44,45,47,48] and references cited therein. For the study of differential equations with nonlocal initial conditions, we refer to the papers [11,12,17,19,20,36,37,39,40,42,44,49,50,52].…”

Optimal controls for a class of impulsive fractional differential equations with nonlocal conditions

“…Since the end of the last century, approximate controllability of problems has been paid more and more attention to [17][18][19][20][21][22]. Impulsive differential equations and optimal conditions have been an active area of research because the impulsive differential system can fully consider the effect of abrupt changes on state.…”

Approximate controllability of fractional nonlinear neutral stochastic differential inclusion with nonlocal conditions and infinite delay

“…Slama and Boudaoui [40] obtained sufficient conditions for the existence of mild solutions for the fractional impulsive stochastic differential equation with nonlocal conditions and infinite delay. For more details see [4,33,39] and the references contained therein.…”