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