Fractional growth models: Malthus and Verhulst

Authors

  • Junior Cesar Alves Soares University State of Mato Grosso
  • Stefânia Jarosz University of Campinas
  • Felix Silva Costa State University of Maranhão

Keywords:

Fractional Malthus equation, Fractional logistic equation, Mittag-leffer fuction, 𝜅-Caputo fractional derivative.

Abstract

This article presents fractional versions for Malthus and Verhulst equations, based on the 𝜅-Caputo fractional derivative. Regarding the Malthus model, we present the analytical solution for the 𝜅-fractional equation. For the logistic equation, we present a numerical solution for 𝜅 → 1 and compare our results with analytical solutions found in literature. Since the numerical results obtained are different from the ones already obtained analytically, we aim to raise some discussion on this matter.

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Published

2022-09-28

How to Cite

SOARES, J. C. A.; JAROSZ, S.; COSTA, F. S. Fractional growth models: Malthus and Verhulst. C.Q.D. - Revista Eletrônica Paulista de Matemática, Bauru, v. 22, n. 2, 2022. Disponível em: https://sistemas.fc.unesp.br/ojs/index.php/revistacqd/article/view/330. Acesso em: 7 jan. 2025.

Issue

v.22, n.2 - Edição Brazilian Symposium on Fractional Calculus – Set/2022

Section

Artigos de Pesquisa

License

Copyright (c) 2022 C.Q.D. - Revista Eletrônica Paulista de Matemática

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.