Un modelo fraccionario para el análisis de setas comestibles: Análisis y simulación usando el esquema L1

Adán Jair Serna-Reyes; Jorge Eduardo Macias-Diaz; Pamela Romo-Rodríguez

doi:10.33064/iycuaa2024934984

Authors

Adán Jair Serna-Reyes Universidad Tecnológica del Norte de Aguascalientes https://orcid.org/0000-0003-3569-6207
Jorge Eduardo Macias-Diaz Universidad Autónoma de Aguascalientes
Pamela Romo-Rodríguez Instituto Tecnológico de Pabellón de Arteaga https://orcid.org/0000-0003-1812-7491

DOI:

https://doi.org/10.33064/iycuaa2024934984

Keywords:

logistic function, Caputo time-fractional derivative, L1 differences, asymptotical stability, order of convergence, fixed point theorem

Abstract

In this research, a generalization of Verhulst’s equation is proposed, to establish a model of fungus growth, the Caputo time-fractional derivative is used to that end. The main property of the logistics function is an asymptotic equilibrium point, it is verified that this generalization also accomplishes this state. With the help of a fixed-point theorem, it is verified the existence of a solution for the numerical method, which utilizes L1 differences, also it is explicit, and convergent to the solution of the continuous system. Some simulations are presented in order to verify the properties previously proved, such as the order of convergence and graphical simulations.

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Author Biographies

Adán Jair Serna-Reyes, Universidad Tecnológica del Norte de Aguascalientes

Dirección Académica de Tecnologías de la Información y Mecatrónica

Pamela Romo-Rodríguez, Instituto Tecnológico de Pabellón de Arteaga

Departamento de Ciencias Básicas

References

• Ali Shah, N., Ahmed, N., Elnaqeeb, T., & Rashidi, M. M. (2019). Magnetohydrodynamic free convection flows with thermal memory over a moving vertical plate in porous medium. Journal of Applied and Computational Mechanics, 5(1), 150-161.

• Brandibur, O., Garrappa, R., & Kaslik, E. (2021). Stability of systems of fractional-order differential equations with Caputo derivatives. Mathematics, 9(8), 914.

• Caputo, M., & Cametti, C. (2021). Diffusion through skin in the light of a fractional derivative approach: progress and challenges. Journal of Pharmacokinetics and Pharmacodynamics, 48(1), 3-19.

• Ding, Y., Wang, Z., & Ye, H. (2011). Optimal control of a fractional-order HIV-immune system with memory. IEEE Transactions on Control Systems Technology, 20(3), 763-769.

• Lin, Y., & Xu, C. (2007). Finite difference/spectral approximations for the time-fractional diffusion equation. Journal of computational physics, 225(2), 1533-1552.

• Macías-Díaz, J. E., Serna-Reyes, A. J., & Flores-Oropeza, L. A. (2024). A stable and convergent finite-difference model which conserves the positivity and the dissipativity of Gibbs’ free energy for a nonlinear combustion equation. Journal of Computational and Applied Mathematics, 437, 115492.

• Ortiz, J. M., & Hernández, L. R. (2013). The theorem existence and uniqueness of the solution of a fractional differential equation. Acta Universitaria, 23, 16-18.

• Ostwald, W. (1883). Studien zur chemischen Dynamik fuer Praktische Chemie, 136 (n.s. 27, 28), 1–39, 449–495.

• Podlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier.

• Real, L. A. (1977). The Kinetics of Functional Response. The American Naturalist, 111(978), 289–300.

• Robertson, T. B. (1908). On the normal rate of growth of an individual, and its biochemical significance. Archiv für Entwicklungsmechanik der Organismen, 25(4), 581-614.

• Sarikaya, A., & Ladisch, M. R. (1997). An unstructured mathematical model for growth of Pleurotus ostreatus on lignocellulosic material in solid-state fermentation systems. Applied biochemistry and biotechnology, 62, 71-85.

• Swan, G. W. (1986). Cancer chemotherapy: Optimal control using the Verhulst-Pearl equation. Bulletin of mathematical biology, 48, 381-404.

• Verhulst, P.F. (1838). Notice sur la loi que la population suit dans son accroissement. Correspondence Mathematique et Physique (Ghent), 10, 113-121.

• Zhuang, P., & Liu, F. (2006). Implicit difference approximation for the time fractional diffusion equation. Journal of Applied Mathematics and Computing, 22, 87-99.