  The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a new
fractional derivative, \[{}^\rho \mathcal{D}_a^\alpha f (x) =
\frac{\rho^{\alpha-n+1}}{\Gamma({n-\alpha})} \, \bigg(x^{1-\rho}
\,\frac{d}{dx}\bigg)^n \int^x_a \frac{\tau^{\rho-1} f(\tau)}{(x^\rho -
\tau^\rho)^{\alpha-n+1}}\, d\tau \] which generalizes two familiar fractional
derivatives, namely, the Riemann-Liouville and the Hadamard fractional
derivatives to a single form. In this paper, we derive the existence and
uniqueness results for a generalized fractional differential equation governed
by the fractional derivative in question.
