In this study, using some new contractions, we obtain an existence and uniqueness conclusion for a fractional differential equation with Atangana-Baleanu derivative as follows:
\begin{align}\label{202}
&(_0^{ABC}D^{\xi}\delta)(s)=h(s,\delta(s)),~~~~~~~~~~~~~~~~~
0\leq s,\xi\leq 1,~~~~~~~~~~~~~~~~\\
\nonumber &\delta(0)=\delta_0,~~~~~~~~~~~~~~~~~
\end{align}
where $^{ABC}D^{\xi}$ is the Atangana-Baleanu derivative of order $\xi$ and
$f$ is continuous with $f(0,\hslash(0))=0$.