Talk:Fractional-order system

Problems

We came here from WikiProject Mathematics, and we can't figure out why this article is here. It's generally well-written as a mathematical survey article, except

1. It uses notation for the fractional derivative, not used elsewhere on Wikipedia, or introduced.
2. I can't follow the formulas.

But, even if that were fixed, it wouldn't make a good Wikipedia article. Perhaps what makes sense should be merged into fractional integral, as it seems to have the same relation to fractional integral as a (continuous) dynamical system has to integral. — Arthur Rubin (talk) 20:04, 9 June 2013 (UTC)

In other words, fractional integral:fractional-order system::integral:dynamical system. — Arthur Rubin (talk) 20:06, 9 June 2013 (UTC)

While the article surely needs some work, the topic of fractional order systems looks like a notable one. Entire books have been written about the topic (such as the book citation I added in the lead) and it is an active area of research. These systems have been studied in a few different contexts: in physics in the context of fractal dynamics, chaos, and power law behavior. On the engineering side, non-inetgral PID controllers are an active area of research and are bound up with fractional order systems. I would recommend against the merge, because the control theory aspects seem far afield of the pure math of the fractional integral. --Mark viking (talk) 21:06, 9 June 2013 (UTC)

Thank you. I appreciate your work, but after I wrote that, I discovered we already have an article fractional dynamics, which is about fractional-order systems. I see the topic is notable, but it seems to be the same topic as fractional dynamics. At the least, they should be merged, and control-system aspects possibly split out again. — Arthur Rubin (talk) 21:13, 9 June 2013 (UTC)

The solution of a fractional-order system should be an implicit fractional integral, as noted in the article:

The solution of:

${^{C}\mathbb {D} _{t}^{\alpha }}x(t)=f(t,x(t)),\quad t\in [0,T],\quad x(0)=x_{0},\quad 0<\alpha <1.$

should be

$_{a}\mathbb {D} _{t}^{-\alpha }f(t,x(t))$

— Arthur Rubin (talk) 12:30, 17 June 2013 (UTC)

Chaotic

This article is chaotic and both very poorly written and presented. This is an interesting subject and it would be helpful if someone with some ability was able to present it in a useful style. Whilst most of us grasp mathematics it is possible for a poor author to obfuscate even the most of simple ideas.

The author of this certainly has introduced a great deal of obfuscation. Please help to fix this. — Preceding unsigned comment added by 101.103.164.85 (talk) 08:08, 8 June 2014 (UTC)