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Geometry of fractional spaces
2012
Advances in Theoretical and Mathematical Physics
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool is fractional calculus, which is cast in a way convenient for the definition of the differential structure, distances, volumes, and symmetries. By an extensive use of concepts and techniques of fractal geometry, we clarify the relation between fractional
doi:10.4310/atmp.2012.v16.n2.a5
fatcat:td44nsj6grbsrhkcrh5ynv7v4e