We can think of classical derivative as a representation of rate of change and when we say $dx/dt$ we mean velocity at time $t$, and $dx^2/dt^2$ acceleration. But when it is fractional order derivative it is vague and difficult to represent it.
I had read GEOMETRIC AND PHYSICAL INTERPRETATIONOF FRACTIONAL INTEGRATION ANDFRACTIONAL DIFFERENTIATION by Podlubny but I am not clear with the physical interprtitation concept. I am thankful if you can help me to understand.
http://people.tuke.sk/igor.podlubny/pspdf/pifcaa_r.pdf
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