Stochastic functional differential equations of Sobolev-type with infinite delay

Stochastic differential equations have been widely used to model a number of phenomena in diverse fields of science and engineering. In this paper, we focus on the local existence of mild solution for a class of stochastic functional differential equations of Sobolev-type with infinite delay. Furthermore, the results are extended to study the local existence results for neutral stochastic differential equations of Sobolev-type. Using the semigroup theory and fixed point argument, we establish a set of sufficient conditions for obtaining the required result. Furthermore, existence results for integro-differential equations of Sobolev-type is also discussed. Finally, an example is provided to illustrate the obtained theory.