Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

• Autorzy: Tadeusz Kosztołowicz , Katarzyna Lewandowska
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

subdiffusion; nonadditive entropy; releasing substane; fractional calculus

• Czasopismo: Open Physics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 645-651

Daty

wydano

2012-06-01

online

2012-06-17

Twórcy

autor

Tadeusz Kosztołowicz

• Institute of Physics, Jan Kochanowski University, ul. Świȩtokrzyska 15, 25-406, Kielce, Poland,

autor

Katarzyna Lewandowska

• Department of Radiological Informatics and Statistics, Medical University of Gdańsk, ul. Tuwima 15, 80-210, Gdańsk, Poland,

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Identyfikatory

DOI

10.2478/s11534-012-0078-z