  Of the many definitions for fractional order differintegral, the
Grunwald-Letnikov definition is arguably the most important one. The necessity
of this definition for the description and analysis of fractional order systems
cannot be overstated. Unfortunately, the Fractional Order Differential Equation
(FODE) describing such a systems, in its original form, highly sensitive to the
effects of random noise components inevitable in a natural environment. Thus
direct application of the definition in a real-life problem can yield erroneous
results. In this article, we perform an in-depth mathematical analysis the
Grunwald-Letnikov definition in depth and, as far as we know, we are the first
to do so. Based on our analysis, we present a transformation scheme which will
allow us to accurately analyze generalized fractional order systems in presence
of significant quantities of random errors. Finally, by a simple experiment, we
demonstrate the high degree of robustness to noise offered by the said
transformation and thus validate our scheme.
