Dynamics of Noninteger Derivative Models

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Abstract
A dynanmic model is generalized by replacing ∇2 by -(-∇2)a where a is in the region 0≤a≤1. The interface velocity is determined by the local curvature for a≪1/2, whereas its equation is nonlocal for a>1/2. The Gibbs-Thomson relation holds for a>1/2. If 0≪ε≡2a-1≪1, we can use an ε-expansion approximation.

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