Ulam–Hyers stability of fractional Itô–Doob stochastic differential equations.

This article is devoted to prove the existence and uniqueness (EU) of solution of fractional Itô–Doob stochastic differential equations (FIDSDE) with order ϰ∈(0,1)$$ \mathrm{\varkappa}\in \left(0,1\right) $$ by using the fixed point technique (FPT). We analyze the Ulam–Hyers stability (UHS) of FIDSDE by using the Gronwall inequality (GI) and the stochastic analysis techniques. We present an application of our results by two theoretical examples. [ABSTRACT FROM AUTHOR]