Affiliation:
1. Balikesir University, Faculty of Science and Arts, Department of Mathematics, Balikesir, Turkey
Abstract
The fractional advection-diffusion equations are obtained from a fractional
power law for the matter flux. Diffusion processes in special types of porous
media which has fractal geometry can be modelled accurately by using these
equations. However, the existing nonlocal fractional derivatives seem
complicated and also lose some basic properties satisfied by usual
derivatives. For these reasons, local fractional calculus has recently been
emerged to simplify the complexities of fractional models defined by nonlocal
fractional operators. In this work, the conformable, a local, well-behaved
and limit-based definition, is used to obtain a local generalized form of
advection-diffusion equation. In addition, this study is devoted to give a
local generalized description to the combination of diffusive flux governed
by Fick?s law and the advection flux associated with the velocity field. As a
result, the constitutive conformable advection-diffusion equation can be
easily achieved. A Dirichlet problem for conformable advection-diffusion
equation is derived by applying fractional Laplace transform with respect to
time t and finite sin-Fourier transform with respect to spatial coordinate x.
Two illustrative examples are presented to show the behaviours of this new
local generalized model. The dependence of the solution on the fractional
order of conformable derivative and the changing values of problem parameters
are validated using graphics held by MATLcodes.
Publisher
National Library of Serbia
Subject
Renewable Energy, Sustainability and the Environment
Cited by
24 articles.
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