Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion |
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Authors: | Tadeusz Kosztołowicz Katarzyna D Lewandowska |
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Institution: | 1.Institute of Physics,Jan Kochanowski University,Kielce,Poland;2.Department of Radiological Informatics and Statistics,Medical University of Gdańsk,Gdańsk,Poland |
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Abstract: | We consider here two different models describing subdiffusion. One of them is derived from Continuous Time Random Walk formalism
and utilizes a subdiffusion equation with a fractional time derivative. The second model is based on Sharma-Mittal nonadditive
entropy formalism where the subdiffusive process is described by a nonlinear equation with ordinary derivatives. Using these
two models we describe the process of a substance released from a thick membrane and we find functions which determine the
time evolution of the amount of substance remaining inside this membrane. We then find ‘the agreement conditions’ under which
these two models provide the same relation defining subdiffusion and give the same function characterizing the process of
the released substance. These agreement conditions enable us to determine the relation between the parameters occuring in
both models. |
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Keywords: | |
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