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The author (Bull. Math. Anal. App. 6(4)(2014):1-15), introduced a newfractional 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 fractionalderivatives, namely, the Riemann-Liouville and the Hadamard fractionalderivatives to a single form. In this paper, we derive the existence anduniqueness results for a generalized fractional differential equation governedby the fractional derivative in question.

Existence and Uniqueness results for a class of Generalized Fractional Differential Equations