A New Approach to Generalized Fractional Derivatives

The author (Appl. Math. Comput. 218 (3): 860-865, 2011) introduced a new fractional integral operator given by, \ (^ρI^α₀+f) (x) = ρ^1- αΓ (α) ˣₐ 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.