On the qualitative behaviors of stochastic delay integro-differential equations of second order

Abstract

Abstract In this paper, we investigate the sufficient conditions that guarantee the stability, continuity, and boundedness of solutions for a type of second-order stochastic delay integro-differential equation (SDIDE). To demonstrate the main results, we employ a Lyapunov functional. An example is provided to demonstrate the applicability of the obtained result, which includes the results of this paper and obtains better results than those available in the literature.

Keywords

• Stability
• Continuity
• Boundedness
• Stochastic delay
• Integro-differential equation
• Lyapunov functional