Fractional Bands uses a modelisation of price variation by a Fractional Brownian Motion, that incorporates the consideration of the Fractal dimension, contrary to the Bollinger Bands, which are based on a Wiener Brownian Motion (a particular case of the Fractional Brownian Motion). They also use a different equation from the Fractal Bands (https://www.mql5.com/en/code/8895). This difference, while being more consistent with the model on a mathematical point of view, does not seem to provide an indicator as interesting at a trading point of view. Nonetheless, it might still be of some use in combination with other indicators.
More details on my blog: http://fractalfinance.blogspot.com/2009/05/fractional-bands.html
Here is the Fractional Bands (in limegreen) with the Fractal Bands (in red), both share the same MA, which is the FRASMA (https://www.mql5.com/en/code/8866):
action just like pressing home key, esc to exit,Fractal Bands
A variation of the Bollinger Bands that incorporates findings from a fractal analysis