Towards Multifractional Calculus
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 comme...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2018-06-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fphy.2018.00058/full |
| _version_ | 1818560587653709824 |
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| author | Gianluca Calcagni |
| author_facet | Gianluca Calcagni |
| author_sort | Gianluca Calcagni |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T00:40:12Z |
| format | Article |
| id | doaj.art-dab40a03df4e4b249203ae9e6949faf7 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-12-14T00:40:12Z |
| publishDate | 2018-06-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-dab40a03df4e4b249203ae9e6949faf72022-12-21T23:24:25ZengFrontiers Media S.A.Frontiers in Physics2296-424X2018-06-01610.3389/fphy.2018.00058362619Towards Multifractional CalculusGianluca CalcagniAfter 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.https://www.frontiersin.org/article/10.3389/fphy.2018.00058/fullquantum gravityfractional calculusfractional derivativesmultiscale geometrymultifractional spacetimes |
| spellingShingle | Gianluca Calcagni Towards Multifractional Calculus Frontiers in Physics quantum gravity fractional calculus fractional derivatives multiscale geometry multifractional spacetimes |
| title | Towards Multifractional Calculus |
| title_full | Towards Multifractional Calculus |
| title_fullStr | Towards Multifractional Calculus |
| title_full_unstemmed | Towards Multifractional Calculus |
| title_short | Towards Multifractional Calculus |
| title_sort | towards multifractional calculus |
| topic | quantum gravity fractional calculus fractional derivatives multiscale geometry multifractional spacetimes |
| url | https://www.frontiersin.org/article/10.3389/fphy.2018.00058/full |
| work_keys_str_mv | AT gianlucacalcagni towardsmultifractionalcalculus |