"...    The strength of derivatives of fractional order is their ability to describe real situations more adequately than integer-order derivatives, especially when the  problem has memory or hereditary properties    ...".

"...   In order to describe our model, let us recall some definitions and results of fractional calculation. For more details see Podlubny (1999).   ..."
Podlubny, I. (1999). Fractiorlal Differential Eqnations. Academic presse, San Diego and California.
(Obviously a spelling error there, and perhaps some French terminology - Fourier series, wavelets , and fractals all originated in France!)

• Benoit Mandelbrots "fractals" (fractional dimensions), and their expressive power in being able to describe reality when most other methods fall far short (mainly known for computer-generated images - trees, mountain ranges, etc)
• scientists' perpetual failures in understanding natural time series (periodicities, spectra), in spite of having tools like [Fourier, wavelet, Hilbert, etc] transforms.  A few rare [mathematicians, statisticians, scientists] are very good, most merely use the standard approaches and tools available.  "Climate change" in the current context has always meant that "CO2 is the primary driver of climate change over the last 150 years", a period that has gradually been whittled down to the last 20 years for at least a few rare scientists who can smell the .   As I had said, "Climate Change" is a catastrophic failure of [rational, logical, scientific] thinking by essentially all government and academic scientists, and the failures in being able to get any handle on natural time series is hilarious (the same also applies to their phenomenological modeling).