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

Abstract

a b s t r a c tIn 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.

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“…In the references (see [6], [7]) can be found several relations and important formulas respect to the fractional derivative, however, for sake of simplicity, we put here only the followings:…”

“…With this aim, we will use the Jumaries's modified Riemann-Lioville derivative of order α (see [6], [7]). This kind of fractional derivative is defined as…”