Exact and approximate solutions of fractional partial differential equations for water movement in soils

Su, Ninghu (2017) Exact and approximate solutions of fractional partial differential equations for water movement in soils. Hydrology, 4 (1). 8. pp. 1-13.

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Abstract

This paper presents solutions of the fractional partial differential equation (fPDE) for analysing water movement in soils. The fPDE explains processes equivalent to the concept of symmetrical fractional derivatives (SFDs) which have two components: the forward fractional derivative (FFD) and backward fractional derivative (BFD) of water movement in soils with the BFD representing the micro-scale backwater effect in porous media. The distributed-order time-space fPDE represents water movement in both swelling and non-swelling soils with mobile and immobile zones with the backwater effect operating at two time scales in large and small pores. The concept of flux-concentration relation is now updated to account for the relative fractional flux of water movement in soils.

Item ID: 47754
Item Type: Article (Research - C1)
ISSN: 2306-5338
Keywords: water movement in soils; random wandering process; symmetrical fractional partial differential equations; micro-scale backwater effect; large-small pores; mobile-immobile zones
Additional Information:

© 2017 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Funders: Distinguished Expert of Ningxia
Date Deposited: 14 Mar 2017 05:26
FoR Codes: 04 EARTH SCIENCES > 0406 Physical Geography and Environmental Geoscience > 040603 Hydrogeology @ 40%
05 ENVIRONMENTAL SCIENCES > 0503 Soil Sciences > 050305 Soil Physics @ 60%
SEO Codes: 96 ENVIRONMENT > 9609 Land and Water Management > 960905 Farmland, Arable Cropland and Permanent Cropland Water Management @ 50%
96 ENVIRONMENT > 9609 Land and Water Management > 960903 Coastal and Estuarine Water Management @ 20%
96 ENVIRONMENT > 9609 Land and Water Management > 960999 Land and Water Management of Environments not elsewhere classified @ 30%
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