Well-posedness and EM approximations for non-Lipschitz stochastic fractional integro-differential equations

Abstract

This paper considers the nonlinear stochastic fractional integro-differential equations (SFIDEs) under the non-Lipschitz conditions, which are general and include many stochastic (fractional) integro-differential equations discussed in literature. An important connection between SFIDEs and stochastic Volterra integral equations (SVIEs) is derived in detail by the Fubini theorem. Using the Euler–Maruyama (EM) approximation, we prove the existence, uniqueness and stability results of the solution to SFIDEs. Moreover, it is shown that the modified EM solution of SFIDEs shares strong first-order sharp convergence. The numerical examples are performed to show the accuracy and effectiveness of the numerical scheme and verify the correctness of our theoretical analysis. • The model covers many nonlinear stochastic (fractional) integro-differential models. • Well-posedness of the models is investigated under the non-Lipschitz condition. • The modified EM approximation of the models admits strong first-order convergence.