The non-linear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization

Volume 1, Issue 1, pp 1--17

Publication Date: 2017-10-22

http://dx.doi.org/10.22436/mns.01.01.01

Authors

J. Hristov - Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia 1756, 8 Kliment Ohridsky, blvd. Bulgaria

Abstract

The Dodson mass diffusion equation with exponentially diffusivity is analyzed through approximate integral solutions. Integral-balance solutions were developed to integer-order versions as well as to formally fractionalized models. The formal fractionalization considers replacement of the time derivative with a fractional version with either singular (Riemann-Liouville or Caputo) or non-singular fading memory. The solutions developed allow seeing a new side of the Dodson equation and to separate the formal fractional model with Caputo-Fabrizio time derivative with an integral-balance allowing relating the fractional order to the physical relaxation time as adequate to the phenomena behind.

Keywords

Non-linear diffusion, singular fading memory, non-singular fading memory, formal fractionalization, integral balance approach

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