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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The fractional Laplacian of a function with respec
t to another function - Arran Fernandez (Eastern M
editerranean University)
DTSTART;TZID=Europe/London:20220222T090000
DTEND;TZID=Europe/London:20220222T093000
UID:TALK167678AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/167678
DESCRIPTION:The fractional Laplacian is a widely used tool in
multi-dimensional fractional PDEs\, useful because
of its natural relationship with the multi-dimens
ional Fourier transform via fractional power funct
ions. A well-known general class of fractional ope
rators is given by fractional calculus with respec
t to functions\; this has usually been studied in
1 dimension\, but here we study how to extend it t
o an $n$-dimensional setting. We also formulate Fo
urier transforms with respect to functions\, both
in 1 dimension and in $n$ dimensions. Armed with t
hese 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.\nJoi
nt work with Joel E. Restrepo (Nazarbayev Universi
ty) and Jean-Daniel Djida (AIMS Cameroon).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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