TL;DR
This paper discusses the development of a multiscale fractional calculus framework motivated by quantum gravity, reviewing current proposals and exploring properties of multifractional Laplacians.
Contribution
It introduces various types of multifractional Laplacians and outlines a program to define scale-dependent fractional operators for quantum gravity applications.
Findings
Different multifractional Laplacians are characterized and compared.
The paper reviews existing proposals for scale-dependent fractional calculus.
It identifies properties and challenges of multifractional operators.
Abstract
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.
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