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Mathematics Subject Classification: Primary: 93D09, 6A33. Secondary: 93B03, 34A26, 42A16.
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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.32 n.1 San José Jan./Mar. 2025
http://dx.doi.org/10.15517/rmta.v32i1.57678
Artículo
A robust stability criterion in the heat equation with a conformable fractional derivative defined on a radially symmetric sphere
Un criterio de estabilidad robusta en la ecuación de calor con una derivada fraccionaria conformable general definida
sobre una esfera radialmente simétrica
1Universidad Autónoma del Estado de Hidalgo, Área Académica de Matemáticas y Física, Mineral de la Reforma, México. E-Mail: temoltzi@uaeh.edu.mx
2Universidad Autónoma del Estado de Hidalgo, Área Académica de Matemáticas y Física, Mineral de la Reforma, México; ravila@uaeh.edu.mx
3Universidad Autónoma del Estado de Hidalgo, Área Académica de Matemáticas y Física, Mineral de la Reforma, México; rcruzc@uaeh.edu.mx
4Universidad Autónoma del Estado de Hidalgo, Área Académica de Matemáticas y Física, Mineral de la Reforma, México; rjimenez@uaeh.edu.mx
5Universidad Autónoma del Estado de Hidalgo, Área Académica de Matemáticas y Física, Mineral de la Reforma, México; almasofia_santillan@uaeh.edu.mex
In this paper, we present a robust stability criterion for a heat equation with axial symmetry and with a general time-conformable fractional derivative defined on a sphere. The heat equation is assumed to have a heat source that is represented as a Fourier series with coefficients described by bounded, piecewise continuous functions. The robust stability criterion establishes conditions to guarantee that the solution of the heat equation, along with its partial derivative with respect to the radial axis and its general time-conformable fractional derivative, remains bounded by a predetermined value. The robust stability criterion is obtained by extending the concept of stability under constant-acting perturbations applied to systems of ordinary differential equations. The results are illustrated numerically.
Keywords: General conformable fractional derivative; Heat equation; Fourier series; Robust stability.
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.
Palabras clave: Derivada fraccionaria conformable general; Ecuación de calor; Series de Fourier; Estabilidad robusta.
Acknowledgments
The authors would like to thank the handling editor and the referees for their helpful and useful comments and suggestions.
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Received: February 16, 2024; Accepted: October 28, 2024
This is an open-access article distributed under the terms of the Creative Commons Attribution License
