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

Abstract

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.