Well posedness of second-order impulsive fractional neutral stochastic differential equations

Abstract

In this manuscript, we investigate a class of second-order impulsive fractional neutral stochastic differential equations (IFNSDEs) driven by Poisson jumps in Banach space. Firstly, sufficient conditions of the existence and the uniqueness of the mild solution for this type of equations are driven by means of the successive approximation and the Bihari's inequality. Next we get the stability in mean square of the mild solution via continuous dependence on initial value.

Keywords

• stochastic fractional differential equations
• bihari's inequality
• successive approximation
• poisson jumps