2004/04/15 by Kwok Sau Fa, Fa, Kwok Sau, E. K. Lenzi +1
Engineering · Mathematics · #FOS: Physical sciences #Fractional Differential Equations Solutions #Nanofluid Flow and Heat Transfer #Numerical methods in engineering #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.cond-mat/0404352
openalex publication_date 2004/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different physical systems like: amorphous semicondutors, polymers, composite heterogeneous films and porous media. They have also been used to calculate the heat load intensity change in blast furnace walls, to solve problems of control theory and dynamic problems of linear and nonlinear hereditary mechanics of solids. In this work, we investigate the scaling properties related to the nonlinear fractional diffusion equations and indicate the possibilities to the applications of these equations to simulate the water transport in unsaturated soils. Usually, the water transport in soils with anomalous diffusion, the dependence of concentration on time and distance may be expressed in term of a single variable given by λq = x/tq. In particular, for q=1/2 the systems obey Fick's law and Richards' equation for water transport. We show that a generalization of Richards' equation via fractional approach can incorporate the above property.