The nonlinear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization

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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.
Integralbalance solutions were developed to integerorder versions as well as to formally fractionalized models. The formal
fractionalization considers replacement of the time derivative with a fractional version with either singular (RiemannLiouville
or Caputo) or nonsingular fading memory. The solutions developed allow seeing a new side of the Dodson equation and
to separate the formal fractional model with CaputoFabrizio time derivative with an integralbalance allowing relating the
fractional order to the physical relaxation time as adequate to the phenomena behind.
Keywords
 Nonlinear diffusion
 singular fading memory
 nonsingular fading memory
 formal fractionalization
 integral balance approach
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