A New Approach to Generalized Fractional Derivatives

Original · EN

The author (Appl. Math. Comput. 218(3):860-865, 2011) introduced a new fractional integral operator given by, (ρIαₐ₊f)(x) = ρ¹⁻ αΓ(α) ∫ˣₐ τρ⁻¹ f(τ) (xρ- τρ)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.