AUTHOR=Calcagni Gianluca 

TITLE=Towards Multifractional Calculus

JOURNAL=Frontiers in Physics

VOLUME=6

YEAR=2018

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00058

DOI=10.3389/fphy.2018.00058

ISSN=2296-424X

ABSTRACT=<p>After motivating the need of a multiscale version of fractional calculus in quantum gravity, we review current proposals and the program to be carried out in order to reach a viable definition of scale-dependent fractional operators. We present different types of multifractional Laplacians and comment on their known or expected properties.</p>