A fractional model for the analysis of edible mushrooms: Analysis and simulation using the L1 scheme
DOI:
https://doi.org/10.33064/iycuaa2024934984Keywords:
logistic function, Caputo time-fractional derivative, L1 differences, asymptotical stability, order of convergence, fixed point theoremAbstract
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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Copyright (c) 2024 Adán Jair Serna-Reyes, Jorge Eduardo Macias-Diaz, Pamela Romo-Rodríguez
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