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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Semigroup properties for multi-dimensional fractional integral operators

## Semigroup properties for multi-dimensional fractional integral operatorsAdd to your list(s) Download to your calendar using vCal - Arran Fernandez (Eastern Mediterranean University)
- Monday 11 April 2022, 09:00-10:00
- Seminar Room 2, Newton Institute.
If you have a question about this talk, please contact nobody. FDE2 - Fractional differential equations One of the most commonly discussed properties for any fractional differintegral operator is whether or not it has a semigroup property: for example, is the halfth integral of the halfth integral equal to the first integral? This question becomes more complicated in the setting of multi-parameter operators: for example, the Prabhakar integrals have a semigroup property in exactly two of their four parameters. We consider a general multi-parameter fractional integral operator with a Fox-Wright kernel function, and catalogue exhaustively all possible subsets of its parameters in which a semigroup property is possible. This integral operator is in general multi-dimensional, its dimension corresponding to the number of gamma functions on the denominator of the Fox-Wright function. In the cases where a semigroup property holds, we are able to construct a corresponding multi-dimensional fractional derivative operator which has the same natural inversion and analytic continuation properties as classical fractional derivatives. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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