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Soluciones analíticas y comportamiento dinámico de sistemas conformables de reacción-difusión fraccional
Azzh Saad Alshehry1, Rasool Shah2, Aisha M Alqahtani1
1Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia.
Scientific reports
|February 19, 2026
Resumen
Este estudio introduce un nuevo método que utiliza el operador fraccional conformable para analizar sistemas fraccionales de reacción-difusión. Los resultados muestran que la reducción del orden fraccional mejora la no localidad y ralentiza la difusión, ofreciendo información sobre procesos de transporte complejos.
Área de la Ciencia:
- Física Matemática
- Dinámica No Lineal
- Cálculo Fraccional
Sus antecedentes:
- Los sistemas fraccionales de reacción-difusión modelan fenómenos complejos con efectos de memoria.
- Los métodos de cálculo clásicos pueden no capturar completamente la dinámica no local inherente a estos sistemas.
- El operador fraccional conformable ofrece un enfoque simplificado para el modelado fraccional.
Objetivo del estudio:
- Investigar analíticamente sistemas fraccionales de reacción-difusión utilizando el operador fraccional conformable.
- Reducir las ecuaciones diferenciales parciales fraccionales a formas diferenciales ordinarias para la derivación de soluciones.
- Validar el marco propuesto comparando las soluciones con el Método de Perturbación Homotópica (HPM).
Principales métodos:
- Aplicación del operador fraccional conformable.
- Uso de transformaciones de similitud para simplificar las ecuaciones rectoras.
- Derivación de soluciones analíticas y aproximadas.
- Comparación con soluciones obtenidas mediante el Método de Perturbación Homotópica (HPM).
Principales resultados:
- Se obtuvieron soluciones analíticas y aproximadas para sistemas fraccionales de reacción-difusión.
- El operador fraccional conformable demostró ser eficiente y preciso para sistemas no lineales.
- Se demostró que la reducción del orden fraccional mejora la no localidad y ralentiza los procesos de difusión.
- El estudio conectó con éxito los enfoques de modelado clásicos y fraccionales.
Conclusiones:
- El operador fraccional conformable es una herramienta poderosa para modelar procesos de orden fraccional con efectos de memoria.
- Este marco proporciona una base teórica sólida para aplicaciones en biología matemática, física química e ingeniería.
- Los hallazgos profundizan la comprensión de los fenómenos de transporte fraccional y la dinámica no local.
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