This paper concerns the boundary value problem for a fractional differential equation involving a generalized Caputo fractional derivative in b−metric spaces. The used fractional operator is given by the kernel k(t, s) = ψ(t) − ψ(s) and the derivative operator 1/ψ0(t) d/dt . Some existence results are obtained based on fixed point theorem of α-φ−Graghty contraction type mapping. In the end, we provide some illustrative examples to justify the acquired results
