Stability, continuability, and boundedness for solutions to the second order stochastic delay integro-differential equation

In this paper, we investigate the sufficient conditions that guarantee the stability, continuability and boundedness of solutions for a type of second order stochastic delay integro-differential equation (SDIDE). To demonstrate the main result, we employ the 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. MSC 2020. 34C11; 34K20; 34D20; 34K50; 60H35.