Cálculo fraccionario en modelado de fenómenos de memoria larga
Palabras clave:
cálculo fraccionario, memoria larga, series temporales, modelación matemática, dependencia temporal, sistemas dinámicos.Resumen
En el análisis de sistemas dinámicos complejos, la problemática central radica en la limitada capacidad de los modelos clásicos para representar fenómenos con memoria larga. El objetivo de esta investigación fue analizar la eficacia del cálculo fraccionario en la modelación de estos procesos, integrando la dependencia temporal en su formulación. Metodológicamente, se adoptó un enfoque no experimental de tipo analítico, sustentado en información proveniente de organismos nacionales e internacionales, junto con la aplicación de ecuaciones diferenciales fraccionarias y técnicas estadísticas avanzadas. Los resultados evidenciaron correlaciones persistentes en múltiples rezagos temporales, rechazo de normalidad en las series analizadas y un ajuste superior de los modelos fraccionarios frente a los modelos tradicionales. Asimismo, se identificó una mayor estabilidad y capacidad predictiva en escenarios de mediano y largo plazo. En síntesis, el cálculo fraccionario permite una representación más precisa de sistemas con memoria larga, superando las limitaciones de los enfoques clásicos.
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Derechos de autor 2024 Elio Jeremy Chiquito Baque (Autor/a)
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-CompartirIgual 4.0.
