We know about the graphical and physical interpretation of the integer order chaotic systems.
Also, fractional order chaotic systems are generalization of the integer order chaotic systems.
But i wonder how can we explicitly describe fractional order chaotic systems?
Anyone please share your knowledge.
If you have derived your fractional differential equations from first principle, this should be clear already for your given system under investigation. But if you have fractionalized the equations out of pure will, then it probably is a mathematical adventure. The "universal" interpretation of regular-fractional DEs is somewhat still lacking, except for a few elegant efforts that have been made by the fractional community. Fractional chaotic systems have yet to be studied from that perspective, I believe.
However, I would like to make a wild (wise?) guess intuitively. If the fractional equation is in time domain, I guess the fractionalization is encoding memory into the nonlinear-chaotic system depending upon the magnitude of the exponent. This could strengthen the deterministic behavior of the chaotic system, and in some cases may transform it to predictable as well in the long run, and hence chaos feature could be compromised.
Dear colleague
It is very difficult to give a geometrical interpretation
of the fractional derivative.
The famous and the first one was given by Igor pudlubny on 2000,
which is named the shadow interpretation.
There exist more, unfortunately they give partial answer.
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