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 calculus and fractals, showing that fractional spaces can be regarded as fractals when the ratio of their Hausdorff and spectral dimension is greater than one. All the results are analytic and constitute the foundation for field theories living on multi-...
Many specialists working in the field of the fractional calculus and its applications simply replace...
This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Unive...
Fractional and fractal derivatives are both generalizations of the usual derivatives that consider d...
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hau...
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectr...
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectr...
Our goal is to prove the existence of a connection between fractal geometries and fractional calculu...
Our goal is to prove the existence of a connection between fractal geometries and fractional calculu...
We show a relation between fractional calculus and fractals, based only on physical and geometrical ...
Local fractional functional analysis is a totally new area of mathematics, and a totally new mathema...
We show a relation between fractional calculus and fractals, based only on physical and geometrical ...
We show a relation between fractional calculus and fractals, based only on physical and geometrical ...
Many specialists working in the field of the fractional calculus and its applications simply replace...
Many specialists working in the field of the fractional calculus and its applications simply replace...
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as ph...
Many specialists working in the field of the fractional calculus and its applications simply replace...
This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Unive...
Fractional and fractal derivatives are both generalizations of the usual derivatives that consider d...
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hau...
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectr...
We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectr...
Our goal is to prove the existence of a connection between fractal geometries and fractional calculu...
Our goal is to prove the existence of a connection between fractal geometries and fractional calculu...
We show a relation between fractional calculus and fractals, based only on physical and geometrical ...
Local fractional functional analysis is a totally new area of mathematics, and a totally new mathema...
We show a relation between fractional calculus and fractals, based only on physical and geometrical ...
We show a relation between fractional calculus and fractals, based only on physical and geometrical ...
Many specialists working in the field of the fractional calculus and its applications simply replace...
Many specialists working in the field of the fractional calculus and its applications simply replace...
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as ph...
Many specialists working in the field of the fractional calculus and its applications simply replace...
This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Unive...
Fractional and fractal derivatives are both generalizations of the usual derivatives that consider d...