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

• Pinto Jiménez, Manuel ^[1] ; Torres Naranjo, Ricardo Felipe ^[2] ; Campillay-Llanos, William ^[3] ; Guevara Morales, Felipe ^[4]
  1. [1] Universidad de Chile

     Universidad de Chile

     Santiago, Chile

     
  2. [2] Universidad Austral de Chile

     Universidad Austral de Chile

     Valdivia, Chile

     
  3. [3] Universidad Católica del Maule

     Universidad Católica del Maule

     Provincia de Talca, Chile

     
  4. [4] Universidad de Atacama

     Universidad de Atacama

     Copiapo, Chile

     

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• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 39, Nº. 6, 2020, págs. 1471-1513
• Idioma: inglés
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• Resumen

  • 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.