Fractional derivatives in spaces of generalized functions

Abstract

We generalize the two forms of the fractional derivatives (in Riemann- Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of distributions. © 2011 Diogenes Co., Sofia.