Approximate controllability of stochastic differential system with non-Lipschitz conditions

Abstract

This paper includes investigation of approximate controllability results for a multi-term time-fractional stochastic differential system in a Hilbert space. A new set of results is obtained with non-Lipschitz conditions of nonlinear functions using the well-known Picard type iterations. The basic tools of fractional calculus, generalization of semigroup, and stochastic analysis techniques have been utilized. Finally, an application is discussed to illustrate the developed theory.

Keywords:

• Fractional calculus
• multi-term time stochastic differential system
• approximate controllability
• generalized semigroup theory
• mild solution

MATHEMATICS SUBJECT CLASSIFICATION 2010:

• 26A33
• 34A08
• 47H10
• 34G20
• 34A12
• 65C30
• 26A33