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

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+, ⊕,⨀) f...

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Autores principales:	Pinto,Manuel, Torres,Ricardo, Campillay-Llanos,William, Guevara-Morales,Felipe
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2020
Materias:	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
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601471
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spelling	oai:scielo:S0716-091720200006014712020-12-02Applications of proportional calculus and a non-Newtonian logistic growth modelPinto,ManuelTorres,RicardoCampillay-Llanos,WilliamGuevara-Morales,Felipe 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.39 n.6 20202020-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601471en10.22199/issn.0717-6279-2020-06-0090
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	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
spellingShingle	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 Pinto,Manuel Torres,Ricardo Campillay-Llanos,William Guevara-Morales,Felipe Applications of proportional calculus and a non-Newtonian logistic growth model
description	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	Pinto,Manuel Torres,Ricardo Campillay-Llanos,William Guevara-Morales,Felipe
author_facet	Pinto,Manuel Torres,Ricardo Campillay-Llanos,William Guevara-Morales,Felipe
author_sort	Pinto,Manuel
title	Applications of proportional calculus and a non-Newtonian logistic growth model
title_short	Applications of proportional calculus and a non-Newtonian logistic growth model
title_full	Applications of proportional calculus and a non-Newtonian logistic growth model
title_fullStr	Applications of proportional calculus and a non-Newtonian logistic growth model
title_full_unstemmed	Applications of proportional calculus and a non-Newtonian logistic growth model
title_sort	applications of proportional calculus and a non-newtonian logistic growth model
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2020
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172020000601471
work_keys_str_mv	AT pintomanuel applicationsofproportionalcalculusandanonnewtonianlogisticgrowthmodel AT torresricardo applicationsofproportionalcalculusandanonnewtonianlogisticgrowthmodel AT campillayllanoswilliam applicationsofproportionalcalculusandanonnewtonianlogisticgrowthmodel AT guevaramoralesfelipe applicationsofproportionalcalculusandanonnewtonianlogisticgrowthmodel
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Applications of proportional calculus and a non-Newtonian logistic growth model

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