A Generalized Diffusion Equation: Solutions and Anomalous Diffusion-Reference-Cited by-同舟云学术

A Generalized Diffusion Equation: Solutions and Anomalous Diffusion

Published:2023-01-17 Issue:2 Volume:8 Page:34
ISSN:2311-5521
Container-title:Fluids
language:en
Short-container-title:Fluids

Author:

Lenzi Ervin K.¹²^ORCID,Somer Aloisi¹^ORCID,Zola Rafael S.³^ORCID,da Silva Luciano R.²⁴^ORCID,Lenzi Marcelo K.⁵^ORCID

Affiliation:

1. Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil

2. National Institute of Science and Technology for Complex Systems, Centro Brasileiro de Pesquisas Físicas, Rio de Janeiro 22290-180, RJ, Brazil

3. Departamento de Física, Universidade Tecnológica Federal do Paraná, R. Marcílio Dias, 635, Apucarana 86812-460, PR, Brazil

4. Departamento de Física, Universidade Federal do Rio Grande do Norte, Natal 59078-900, RN, Brazil

5. Departamento de Engenharia Química, Universidade Federal do Paraná, Curitiba 80060-000, PR, Brazil

Abstract

We investigate the solutions of a generalized diffusion-like equation by considering a spatial and time fractional derivative and the presence of non-local terms, which can be related to reaction or adsorption–desorption processes. We use the Green function approach to obtain solutions and evaluate the spreading of the system to show a rich class of behaviors. We also connect the results obtained with the anomalous diffusion processes.

Funder

CNPq

National Institute of Science and Technology of Complex Systems-INCT-SC

National Institute of Science and Technology of Complex Fluids-INCT-FCx

LAMAP-UTFPR

Publisher

MDPI AG

Subject

Fluid Flow and Transfer Processes,Mechanical Engineering,Condensed Matter Physics

Link

https://www.mdpi.com/2311-5521/8/2/34/pdf

Reference61 articles.

1. Hilfer, R. (2000). Applications of Fractional Calculus in Physics, World Scientific.

2. Meerschaert, M.M., and Sikorskii, A. (2019). Stochastic Models for Fractional Calculus, de Gruyter.

3. Tarasov, V.E. (2011). Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer Science & Business Media.

4. Fractional calculus in bioengineering, part 1;Magin;Crit. Rev. Biomed. Eng.,2004

5. Herrmann, R. (2011). Fractional Calculus: An Introduction for Physicists, World Scientific.

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