Non-Lipschitz Sobolev Type Fractional Neutral Impulsive Stochastic Differential Equations with Fractional Stochastic Nonlocal Condition, Infinite Delay and Poisson Jumps

摘要

In the present paper, we have established the existence and uniqueness of mild solutions for non-Lipschitz Sobolev type fractional neutral impulsive stochastic differential equations satisfying fractional stochastic nonlocal condition with infinite delay and Poisson jumps in ?p space. we adopt the non-Lipschitz condition proposed by Taniguchi (2009) which is a much weaker condition with wider range of applications. The existence of mild solutions is established by using strong and powerful tool called Picard’s approximation technique. We can find that the similar existence results are suitable for those non-Lipschitz Sobolev type fractional neutral impulsive stochastic differential equations satisfying fractional stochastic nonlocal condition of different fractional orders with infinite delay and Poisson jumps in ?p space. At the end an example is given to illustrate the theory.