Probably not what you are looking for but interesting:
A lot of restrictions of classical calculus is pointed out by Blas M.
Vinagre and YangQuan Chen, starting from the following famous quotes
given by the Procrustes Bed :“all people must fit the same bed, if
tall, cut the legs and if short, stretch the leg” and second one by
the Purloined Letter :“same methods must be always successfully
applicable, if no solution is found, there is no solution”. If these
two cases are not obvious, then one has to look towards a new paradigm
and revisit the origins of classical one. One can see the same history
behind the fractional order modeling and control over classical
From book: Bandyopadhyay, Bijnan, and Shyam Kamal. "Essence of fractional order calculus, physical interpretation and applications." Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach. Springer International Publishing, 2015. 1-54.