Applications of proportional calculus and a non-Newtonian logistic growth model

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-06-0090

Keywords:

Proportional arithmetic, Proportional calculus and proportional derivative and integral , Geometric difference, Geometric integer, Proportional differential equations, Proportional wave equation, Proportional heat equation, Proportional logistic growth

Abstract

On the set of positive real numbers, multiplication, represented by ?, is considered as an operation associated with the notion of sum, and the operation a ? b = aln(b) represents the meaning of the traditional multiplication. The triple (R+, ?,?) forms an ordered and complete field in which derivative and integration operators are defined analogously to the Differential and Integral Calculus. In this article, we present the proportional arithmetic and we construct the theory of ordinary proportional differential equations. A proportional version of Gronwall inequality, Gompertz’s function, the q-Periodic functions, proportional heat, and wave equations as well as a proportional version of Fourier’s series are presented. Furthermore, a non-Newtonian logistic growth model is proposed.

Author Biographies

Manuel Pinto Jiménez, Universidad de Chile.

Dept. de Matemáticas, Fc. de Ciencias.

Ricardo Felipe Torres Naranjo, Universidad Austral de Chile.

Instituto de Ciencias Físicas y Matemáticas, Fc. de Ciencias.

William Campillay-Llanos, Universidad Católica del Maule.

Dept. de Matemática, Física y Estadística, Fc. de Cs. Básicas.

Felipe Guevara Morales, Universidad de Atacama.

Dept. de Matemática.

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Published

2020-11-12

How to Cite

[1]
M. Pinto Jiménez, R. F. Torres Naranjo, W. Campillay-Llanos, and F. Guevara Morales, “Applications of proportional calculus and a non-Newtonian logistic growth model”, Proyecciones (Antofagasta, On line), vol. 39, no. 6, pp. 1471-1513, Nov. 2020.

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