Recent content by mdo

The proposed series can be considered as a special case of the called Mittag-Leffler function (for x>0) or of the alpha-exponential. They appear when we try to solve the equation Dαf(t)+af(t) = δ(t) For interested people I can send papers mdo@fct.unl.pt

Well I suggest you to read a good book on Signals and Systems. There are lots, e.g. Oppenheim+Wilsky, Haykin+Van Veen, Lindner, Roberts. You'll see that linear systems are chartacterised by an impulse response and a transfer function. The transfer function of a fractional derivative is H(s) = sα...

Not exactly. The fractional derivatives are operators with long (infinite) memory. Even with short duration functions the corresponding derivatives have infinite duration. In fact, the local property is lost but all the others are valid, mainly the commutativity.

Of course, the first.

You have a function f(t) that has a Fourier transform, F(ω), that is null or almost null for |ω| > Ω. f(t) is sampled at every multiple of a given interval h to obtain a discrete signal f(n) = f(nh), where h should be < π/Ω. When you compute the DFT, F(μ), you are working on a normalized domain...

I work in Fractional Calculus, since 1994, firstly as a hobby, and in the last 10 years I've published papers regularly. The posed question has some interest and has motivated some attempts, although not completely satisfactory. I do not care about geometric interpretations. Most of the attempts...