Towards multifractional calculus

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.

10 pages; v2: small clarifications and references added

References in corpus (4)

• Dimension and Dimensional Reduction in Quantum Gravity
• Multifractional theories: an unconventional review
• Multiscale spacetimes from first principles
• Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime

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• Newtonian Fractional-Dimension Gravity and Rotationally Supported Galaxies
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• Newtonian Fractional-Dimension Gravity and Disk Galaxies
• Non-local Lagrangian Mechanics: Noether theorem and Hamiltonian formalism
• Representations of the fractional d'Alembertian and initial conditions in fractional dynamics
• On observational signatures of multi-fractional theory
• Cosmology of fractional gravity
• Relativistic Fractional-Dimension Gravity
• Joining Spacetimes on Fractal Hypersurfaces