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 $f(0,\hslash(0))=0$.
