I am trying to find real world applications for fractional derivatives. Where can I find real data (like in a table) where the dynamics is modeled by a fractional derivative operator?
Fractional order differential equations are a generalization of our conventional differential equations that extend our notion of modeling the real world around us. There are many processes in nature that can be more accurately modeled using fractional order derivatives. It has been experimentally demonstrated that the charging and discharging of lossy capacitors for example, follows inherently fractional order dynamics. The flow of fluid in a porous media, voltage-current relation in a semi infinite transmission line etc. are all such examples where the governing equations can be modeled more accurately using fractional order differential operators.
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