TY - JOUR AU - Hristov, Jordan PY - 2017 TI - The non-linear Dodson diffusion equation: Approximate solutions and beyond with formalistic fractionalization JO - Mathematics in Natural Science SP - 1--17 VL - 1 IS - 1 AB - 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. SN - ISSN 2600-7665 UR - http://dx.doi.org/10.22436/mns.01.01.01 DO - 10.22436/mns.01.01.01 ID - Hristov2017 ER -