Well-posedness and stability of fractional stochastic integro-differential equations with general memory effects

Most existing research on well-posedness and stability has focused on fractional stochastic differential equations, with relatively fewer studies addressing fractional stochastic integro-differential equations (FSIDEs). In this work, we address this gap by establishing theoretical results on the well-posedness of FSIDEs. In particular, we derive a generalized Grönwall inequality and present results on Ulam-Hyers stability (UHS). Moreover, we extend existing findings by incorporating both the $ \Phi $-Caputo fractional derivative and the $ \mathrm{p} $th moment, thereby unifying and generalizing current results in the literature.