WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 20, 2025
On Numerical Schemes for Solving Fractional Advection-diffusion Equations in the Sense of Caputo
Authors: , ,
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Abstract: This paper presents the application of concentration described by the fractional
advection-diffusion equation, considering fractional derivatives in the sense of Caputo and a new modified
fractional derivative also in the sense of Caputo. Specifically, approximations of fractional derivatives of
order α $$(m−1≤α≤m, m∈ \mathbb{N}∗)$$ using the finite difference method in the two aforementioned cases have
enabled us to develop numerical resolution schemes. The results of comparative numerical tests between
the two schemes showed that, with the modified Caputo derivative, diffusion is slightly faster with a lower
concentration at the center, unlike the Caputo derivative, which produces slower (anomalous) diffusion
with a higher concentration at the center.
Keywords:
Fractional derivative, Caputo derivative, Fractional calculus, Advection diffusion equation, Numerical methods, finite difference method
Pages: 305-328
DOI: 10.37394/23203.2025.20.34