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