Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler–Maruyama approximation

<p style='text-indent:20px;'>This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to establishing some fine estimates include all cases Abel-type Firstly, existence, uniqueness and continuous dependence on true solution under local Lipschitz condition linear growth are derived in detail. Secondly, Euler–Maruyama method developed for solving numerically equation, then its strong convergence proven same conditions as well-posedness. Moreover, we obtain accurate rate this global condition. In particular, can reach first-order superconvergence when <inline-formula><tex-math id="M1">\begin{document}$ \alpha = 1 $\end{document}</tex-math></inline-formula>. Finally, several numerical tests reported verification theoretical findings.</p>