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On a robust stability criterion in the subdiffusion equation with Caputo–Dzherbashian fractional derivative

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Abstract

This paper presents a robust stability criterion for the subdiffusion equation with Caputo–Dzherbashian fractional derivative. The criterion is obtained by extending the concept of stability under constant-acting perturbations applied to systems of differential equations of integer order. It is assumed that the subdiffusion equation admits external sources that are represented by Fourier series. The robust stability criterion makes it possible to ensure that the solution of the subdiffusion equation, as well as its Caputo–Dzherbashian fractional derivative and its first partial derivative with respect to the longitudinal axis, are bounded.

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  1. In the literature, the fractional derivative of Caputo–Dzherbashian is also called the fractional derivative of Caputo–Djrbashian or fractional derivative of Caputo. In [9], some contributions of Dzherbashian to fractional calculus are presented.

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  1. Área Académica de Matemáticas y Física, Universidad Autónoma del Estado de Hidalgo, Pachuca-Tulancigo Km 4.5, 42184, Mineral de la Reforma, Hidalgo, Mexico

    R. Temoltzi-Ávila

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Temoltzi-Ávila, R. On a robust stability criterion in the subdiffusion equation with Caputo–Dzherbashian fractional derivative. Bol. Soc. Mat. Mex. 29, 74 (2023). https://doi.org/10.1007/s40590-023-00548-6

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