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Hydrology 2017, 4(1), 8; doi:10.3390/hydrology4010008

Exact and Approximate Solutions of Fractional Partial Differential Equations for Water Movement in Soils

College of Science and Engineering, TropWater, and the Cairns Institute, James Cook University, Cairns 4870, Queensland, Australia
Academic Editor: Abdon Atangana
Received: 20 December 2016 / Revised: 12 January 2017 / Accepted: 18 January 2017 / Published: 25 January 2017
(This article belongs to the Special Issue Groundwater Flow)
View Full-Text   |   Download PDF [653 KB, uploaded 25 January 2017]   |  

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. View Full-Text
Keywords: water movement in soils; random wandering process; symmetrical fractional partial differential equations; micro-scale backwater effect; large-small pores; mobile-immobile zones water movement in soils; random wandering process; symmetrical fractional partial differential equations; micro-scale backwater effect; large-small pores; mobile-immobile zones
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Su, N. Exact and Approximate Solutions of Fractional Partial Differential Equations for Water Movement in Soils. Hydrology 2017, 4, 8.

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