Sobolev-type fractional stochastic differential equations with non-Lipschitz coefficients

This paper investigates the existence and uniqueness of mild solutions for a class of nonlinear fractional Sobolev-type stochastic differential equations in Hilbert spaces. In this work, we used the fractional calculus, semigroup theory and stochastic analysis techniques for obtaining the required result. A new set of sufficient condition is established with the coefficients in the equations satisfying some non-Lipschitz conditions, which include classical Lipschitz conditions as special cases. More precisely, the results are obtained by means of standard Picard’s iteration. Finally, an example is given to illustrate the obtained theory.