Katugampola, Udita N. A new approach to generalized fractional derivatives. (English) Zbl 1317.26008 Bull. Math. Anal. Appl. 6, No. 4, 1-15 (2014). Summary: In [Appl. Math. Comput. 218, No. 3, 860–865 (2011; Zbl 1231.26008)], we introduced a new fractional integral operator given by \[ (\rho \mathcal I^{\alpha}_{a+}f)(x) = \frac {\rho^{1-\alpha}}{\Gamma(\alpha)} \int^x_a \frac {\tau^{\rho-1}f(\tau)}{(x^{\rho}-\tau^{\rho})^{1-\alpha}}d\tau, \] 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. Cited in 1 ReviewCited in 96 Documents MSC: 26A33 Fractional derivatives and integrals 65R10 Numerical methods for integral transforms 44A15 Special integral transforms (Legendre, Hilbert, etc.) Keywords:fractional calculus; generalized fractional derivatives; Riemann-Liouville fractional derivative; Hadamard fractional derivative; Erdélyi-Kober operator; Taylor series expansion PDF BibTeX XML Cite \textit{U. N. Katugampola}, Bull. Math. Anal. Appl. 6, No. 4, 1--15 (2014; Zbl 1317.26008) Full Text: Link arXiv