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SUMMARY:Fractional-order differentiation meets generalized probabilities -
  Igor  Podlubny (Technical University of Kosice)
DTSTART:20241211T140000Z
DTEND:20241211T150000Z
UID:TALK222061@talks.cam.ac.uk
DESCRIPTION:Fractional-order derivatives and integrals are suitable tools 
 for modelling in various fields (viscoelastic materials\, hereditary effec
 ts\, anomalous diffusion\, electrochemistry\, and other fields). The Monte
  Carlo method for numerical evaluation of fractional-order derivatives is 
 presented. The main idea consists of using the Gr&uuml\;nwald&ndash\;Letni
 kov approximation and interpreting its coefficients as probabilities. Thos
 e probabilities turn to be signed probabilities: some are positive\, some 
 other are negative. First\, the Monte Carlo method for fractional differen
 tiation of orders between 0 and 1 is considered\; in this case\, all neces
 sary probabilities are of the same sign. For orders above one\, some proba
 bilities become negative\, and some are necessarily greater than one\, and
  we demonstrate how to deal with them. The presented method allows further
  improvements and extensions (including parallel computations)\, and appli
 cations in fractional-order modelling. The talk is based on the joint resu
 lts with Nikolai Leonenko (Cardiff University).&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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