"Once we understand how to relate fractional calculus between different observers or coordinate systems, a clear interpretation of physics applications will become straightforward and meaningful."
– Ehab Malkawi, United Arab Emirates University
The elaboration of methods of analysis different from the traditional ones have been born almost simultaneously with the traditional concepts of infinitesimal calculus; the possibility to introduce derivatives of fractional order, the existence of fractional dimensions, continuous but non-differentiable functions, etc., have been well known for a long time now. But since the last years of the previous century, these non-orthodox concepts are mushrooming and becoming accessible to the wider scholarly community as a consequence of the fast development of computers, and the emergence of concepts such as complexity, fractality, self-organized criticality, and many others that invade not only the fields of mathematics and physics, but also the whole of human knowledge, including the arts and humanities, are becoming so transdisciplinary that it is now familiar to see fractional differential operators as the main tools to investigate any aspect of our present culture.
– José Weberszpil, Universidade Federal Rural do Rio de Janeiro-UFRRJ