Some Results on Backward Stochastic Differential Equations of Fractional Order

In this article, we deal with fractional stochastic differential equations, so-called Caputo type backward equations (Caputo fBSDEs, for short), and study the well-posedness of an adapted solution to fBSDEs order $$\alpha \in (\frac{1}{2},1)$$ whose coefficients satisfy a Lipschitz condition. A novelty article is that introduce new weighted norm in square integrable measurable function space useful proving fundamental lemma its well-posedness. For class systems, then show coincidence between notion Volterra integral equation mild solution.