A New Approach to Generalized Fractional Derivatives
Abstract
The author \mbox{(Appl. Math. Comput. 218(3):860865, 2011)} introduced a new fractional integral operator given by, \[ \big({}^\rho \mathcal{I}^\alpha_{a+}f\big)(x) = \frac{\rho^{1 \alpha }}{\Gamma({\alpha})} \int^x_a \frac{\tau^{\rho1} f(\tau) }{(x^\rho  \tau^\rho)^{1\alpha}}\, d\tau, \] which generalizes the wellknown RiemannLiouville and the Hadamard fractional integrals. In this paper we present a new fractional derivative which generalizes the familiar RiemannLiouville 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 arXiv:
 arXiv:1106.0965
 Bibcode:
 2011arXiv1106.0965K
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 Mathematics  Combinatorics;
 26A33
 EPrint:
 12 Pages, 2 Figures