@article {OA4748,
	title = {Complex Gr{\"u}nwald?Letnikov, Liouville, Riemann?Liouville, and Caputo derivatives for analytic functions},
	journal = {Communications in Nonlinear Science and Numerical Simulation},
	year = {2011},
	note = {n/a},
	abstract = {<p>The well-known Liouville, Riemann?Liouville and Caputo derivatives are extended to the complex functions space, in a natural way, and it is established interesting connections between them and the Gr{\"u}nwald?Letnikov derivative. Particularly, starting from a complex formulation of the Gr{\"u}nwald?Letnikov derivative we establishes a bridge with existing integral formulations and obtained regularised integrals for Liouville, Riemann?Liouville, and Caputo derivatives. Moreover, it is shown that we can combine the procedures followed in the computation of Riemann?Liouville and Caputo derivatives with the Gr{\"u}nwald?Letnikov to obtain a new way of computing them. The theory we present here will surely open a new way into the fractional derivatives computation.</p>
},
	url = {http://oa.uninova.pt/4748/},
	author = {Manuel Duarte Ortigueira and Luis Rodr{\'\i}guez-Germ{\'a} and Juan J. Trujillo}
}
