A New Approach to Generalized Fractional Derivatives

The author mbox{(Appl. Math. Comput. 218(3):860-865, 2011)} introduced a new fractional integral operator given by, [ big({}^ρmathcal{I}^α_{a+}fbig)(x) = frac{ρ^{1- α}}{Γ(α)} int^x_a frac{τ^{ρ-1} f(τ) }{(x^ρ- τ^ρ)^{1-α}}, dτ, ] which generalizes the well-known Riemann-Liouville and the Hadamard fractional integrals. In this paper we present a new fractional derivative which generalizes the familiar Riemann-Liouville and the Hadamard fractional derivatives to a single form. We also obtain two representations of the generalized derivative in question. An example is given to illustrate the results.