Approximate controllability of second-order non-autonomous stochastic impulsive differential systems

Abstract

This paper is concerned with existence, uniqueness, and approximate controllability of mild solutions to second-order non-autonomous stochastic impulsive differential systems. The impulsive differential systems may provide mathematical models to the phenomena having discontinuous jumps. The main results are carried out by using the generalized Banach contraction principle, evolution family, and stochastic analysis. Finally, an example is given to illustrate the results.

Keywords:

• Approximate controllability
• evolution family
• impulsive differential equation
• non-autonomous system
• stochastic differential equation

MATHEMATICS SUBJECT CLASSIFICATION 2010:

• 34G20
• 34K30
• 47H10
• 93B05

Additional information

Funding

The research work of the first author is supported by the “Ministry of Human Resource and Development, India under grant number MHR-02-23-200-44”.