Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions

In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouvile definition of fractional derivatives, one (Jumarie) has proposed recently an alternative referred to as a modified Riemann-Liouville definition, which directly, provides a Taylor's series of fractional order for non differentiable functions. This fractional derivative provides a fractional calculus parallel with the classical one, which applies to non-differentiable functions: and the present short article summarizes the main basic formulae so obtained. (C) 2008 Elsevier Ltd. All rights reserved.