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<p>With a perspective of interest in the modeling of dynamic processes, here we investigate various types of basic growth equations, which in their formulation quantify the change of the variables, the state, or the independent one, using balance equations in which the counts (aggregation-reduction) are of the multiplicative type. We enter the context of the “differential” equations typical of non-Newtonian calculations, such as geometric calculus, bi-geometric calculus, or the lesser-known logarithmic calculus, when we take the step to the limit. In these new possibilities of dynamic laws, we highlight the interpretive aspects. A particular case is to review the equivalents of the logistic equation of the standard calculation in the new accounting calculations, where we make graphical and semantic comparisons. Finally, the construction of a geometric type equation is exemplified, with applications inherent to the financial mathematics.</p>

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Exploring growth models with multiplicative counting: Connections with the geometric and bigeometric calculi

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Fernando Córdova-Lepe,
  • Nicole Martínez-Jeraldo,
  • Ledyz Cuesta-Herrera

摘要

With a perspective of interest in the modeling of dynamic processes, here we investigate various types of basic growth equations, which in their formulation quantify the change of the variables, the state, or the independent one, using balance equations in which the counts (aggregation-reduction) are of the multiplicative type. We enter the context of the “differential” equations typical of non-Newtonian calculations, such as geometric calculus, bi-geometric calculus, or the lesser-known logarithmic calculus, when we take the step to the limit. In these new possibilities of dynamic laws, we highlight the interpretive aspects. A particular case is to review the equivalents of the logistic equation of the standard calculation in the new accounting calculations, where we make graphical and semantic comparisons. Finally, the construction of a geometric type equation is exemplified, with applications inherent to the financial mathematics.