  This paper is concerned with a class of nonlinear boundary value problem
involving fractional derivative in the $\varphi$-Riemann-Liouville sense. Some
Properties of the Green's function for this problem are mentioned. By means of
the Banach contraction principle in $b$-metric space and the technique of the
$\gamma$-$\psi$- Geraghty contractive maps, existence and uniqueness results
are obtained. Two examples are given to support the theoretical results.
