TY  - JOUR
AU  - Aly, Elkhateeb S.
AU  - Liaqat, Muhammad Imran
AU  - Alshammari, Saleh
AU  - El-Morshedy, Mahmoud
PY  - 2025
TI  - Well-posedness and stability of fractional stochastic integro-differential equations with general memory effects
JO  - AIMS Mathematics
SP  - 22265
EP  - 22293
VL  - 10
IS  - 9
AB  - 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    Φ-Caputo fractional derivative and the        p  th moment, thereby unifying and generalizing current results in the literature.
UR  - https://doi.org/10.3934/math.2025992
DO  - 10.3934/math.2025992