"Fractional Tuning" of the Riccati Equation

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Abstract
The dynamics of a free-falling body in complex materials such as a polymer fluid is phenomenologically modeled using a fractional generalization of the Riccati equation. The solution exhibits a rich behavior in its parametric dependence, and unlike normal free–fall there is no terminal velocity, instead a power–law increase in time is obtained. Within this approach the fractional order allows to tune the resulting equation.

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