The fractional Laplacian of a function with respect to another function – Arran Fernandez (Eastern Mediterranean University)

When:
February 22, 2022 @ 9:00 am – 9:30 am
2022-02-22T09:00:00+00:00
2022-02-22T09:30:00+00:00
Where:
Seminar Room 1
Newton Institute

The fractional Laplacian is a widely used tool in multi-dimensional fractional PDEs, useful because of its natural relationship with the multi-dimensional Fourier transform via fractional power functions. A well-known general class of fractional operators is given by fractional calculus with respect to functions; this has usually been studied in 1 dimension, but here we study how to extend it to an $n$-dimensional setting. We also formulate Fourier transforms with respect to functions, both in 1 dimension and in $n$ dimensions. Armed with these building blocks, it is possible to construct fractional Laplacians with respect to functions, both in 1 dimension and in $n$ dimensions. These operators can then be used for posing and solving some generalised families of fractional PDEs.

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