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

dc.creatorPinto Jiménez, Manuel
dc.creatorTorres Naranjo, Ricardo Felipe
dc.creatorCampillay-Llanos, William
dc.creatorGuevara Morales, Felipe
dc.date2020-11-12
dc.date.accessioned2021-01-29T12:45:34Z
dc.date.available2021-01-29T12:45:34Z
dc.identifierhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3783
dc.identifier10.22199/issn.0717-6279-2020-06-0090
dc.identifier.urihttps://revistaschilenas.uchile.cl/handle/2250/163978
dc.descriptionOn 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.en-US
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad Católica del Norte.en-US
dc.relationhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/3783/3582
dc.rightsCopyright (c) 2020 Manuel Pinto Jiménez, Ricardo Felipe Torres Naranjo, William Campillay-Llanos, Felipe Guevara Moralesen-US
dc.rightshttp://creativecommons.org/licenses/by/4.0en-US
dc.sourceProyecciones (Antofagasta, On line); Vol. 39 No. 6 (2020); 1471-1513en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 39 Núm. 6 (2020); 1471-1513es-ES
dc.source0717-6279
dc.source10.22199/issn.0717-6279-2020-06
dc.subjectProportional arithmeticen-US
dc.subjectProportional calculus and proportional derivative and integralen-US
dc.subjectGeometric differenceen-US
dc.subjectGeometric integeren-US
dc.subjectProportional differential equationsen-US
dc.subjectProportional wave equationen-US
dc.subjectProportional heat equationen-US
dc.subjectProportional logistic growthen-US
dc.subject26A15en-US
dc.subjectContinuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variableen-US
dc.subject26A24en-US
dc.subjectDifferentiation (real functions of one variable): general theory, generalized derivatives, mean value theoremsen-US
dc.subject26A42en-US
dc.subjectIntegrals of Riemann, Stieltjes and Lebesgue typeen-US
dc.subject34A30en-US
dc.subjectLinear ordinary differential equations and systems, generalen-US
dc.subjectPeriodic solutions to functional-differential equationsen-US
dc.subject34K13en-US
dc.subject34K25en-US
dc.subjectAsymptotic theory of functional-differential equationsen-US
dc.subject35A08en-US
dc.subjectFundamental solutions to PDEsen-US
dc.subject35A09en-US
dc.subjectClassical solutions to PDEsen-US
dc.subject42A16en-US
dc.subjectFourier coefficients, Fourier series of functions with special properties, special Fourier seriesen-US
dc.titleApplications of proportional calculus and a non-Newtonian logistic growth modelen-US
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US
dc.typetexten-US


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