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Vol. 15 Núm. 2 (2024)
Vol. 15 Núm. 2 (2024): Vol 15, Núm.2 (2024): Julio-Diciembre

Artículos de investigación / Research papers

Numfracpy, Técnicas del C´álculo Fraccionario en Python

https://doi.org/10.19053/uptc.01217488.v15.n2.2024.17346

Publicado 2024-07-23

  • Jorge Hernán López Melo
    • ,
  • Alejandro P. Riascos

Jorge Hernán López Melo
Departamento de Física, Universidad de Nariño

Alejandro P. Riascos
Universidad Nacional de Colombia image/svg+xml

Resumen

En este trabajo se introduce una librería en el lenguaje Python que implementa técnicas propias del cálculo
fraccionario. Este tipo de cálculo ha visto un incremento notable de sus aplicaciones en diversas áreas de
las ciencias en las últimas décadas. Sin embargo, el tipo de cálculos que se necesitan para su desarrollo no
son simples y no hay muchas ayudas computacionales para su implementación, especialmente en Python.
Numfracpy se encuentra disponible al público en el índice de paquetes PyPI (Python Package Index) e
implementa diversos conceptos del cálculo fraccionario como lo son: La integral y la derivada de Riemann-
Liouville, la derivada de Caputo, la derivada de Grünwald-Letnikov, las funciones de Mittag-Leffler, la
solución numérica de un tipo de ecuación diferencial en derivadas fraccionarias y un sistema de tales
ecuaciones diferenciales. En este trabajo se presentan varios algoritmos implementados y los resultados
obtenidos se comparan con aquellos reportados en la literatura, encontrando una buena aproximación en los
diferentes ejemplos ilustrados.

Palabras clave

Cálculo Fraccionario, Caputo, Grünwald-Letnikov, Métodos Numéricos, Python, Riemann-Liouville

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