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.

Keywords:

• Approximate controllability
• fractional calculus
• stochastic differential inclusions
• infinite delay
• multivalued maps

AMS Subject Classifications:

• 34G20; 93B05; 93E03

Notes

No potential conflict of interest was reported by the authors.