Palabras clave
Ecuación de calor
Series de Fourier
Estabilidad robusta
General conformable fractional derivative
Heat equation
Fourier series
Robust stability
Cómo citar
Resumen
En este artículo, presentamos un criterio de estabilidad robusta para una ecuación de calor con simetría axial y con derivada fraccionaria general conformable en el tiempo definida en una esfera. Se supone que la ecuación de calor admite una fuente de calor externa que se representa como una serie de Fourier con coeficientes descritos por funciones continuas a trozos y acotadas. El criterio de estabilidad robusta establece condiciones para garantizar que la solución de la ecuación de calor, así como su derivada parcial con respecto al eje radial y su derivada fraccionaria conformable general en el tiempo, son funciones acotadas por un valor constante prefijado. El criterio de estabilidad robusta se obtiene por una extensión del concepto de estabilidad bajo perturbaciones de acción constante que se aplica a sistemas de ecuaciones diferenciales ordinarias. Los resultados se ilustran numéricamente.
Citas
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Derechos de autor 2025 Raúl Temoltzi-Ávila, Roberto Ávila-Pozos, Ricardo Cruz-Castillo, Ronald R. Jiménez-Munguía, Alma S. Santillán-Hernández