
8:56 PM (0 minutes ago)



I’m looking closely at the nature of the twoparameter MittagLeffler under fractional differentiation for some understanding. We can note that this relation, in snapshot of attached paper, shows an important thing regards the effect on the MittagLeffler parameters a,b of fractional differentiation by D_t^alpha:
In other words, the power of t changes and the MittagLeffler second parameter changes. To me this suggests that rather than power law, the MittagLeffler function mixed with powers is the key function; but there is also the Laplace transform that turns fractional derivatives to multiplication by fractional powers in the transformedspace:
Laplace{( D_t^alpha – beta ) u}(p) = p^alpha Laplace{u} – beta*Laplace{u}
n<length(v)
t<seq(1,n)**alpha
Ok this looks like a more promising manner in which to fit data!!
Sir, since 1995 when I held my first job at Lehman Brothers Fixed Income Research with a great deal of quant work done, this is the first time in this time that I think there is a real science in finance that is deep and it’s in global financial volatility and we’re close to making a breakthrough in this and related areas if we can prove that volatility can be modeled as a perturbation of deterministic FDE.
Preview attachment jumariefractionalvariationaltheory.pdf
Preview attachment LoverroFractionalCalculus.pdf
Preview attachment caputoderivativesdevelopment.pdf
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