On a robust stability criterion in the Cattaneo-Hristov diffusion equation

Abstract

The aim of this paper is to establish a robust stability criterion in the Cattaneo-Hristov diffusion equation moving over an interval under the influence of heat sources. The robust stability criterion arises as a generalization of the definition of stability under constant-acting perturbations that is employed in systems of differential equations. The criterion obtained allows to ensure that the solution of the Cattaneo-Hristov diffusion equation and its first partial derivatives with respect to the longitudinal axis and with respect to time can be bounded by a constant whose value is defined a priori. The criterion is illustrated by a numerical example.

Keywords

Cattaneo-Hristov diffusion equation / Caputo-Fabrizio fractional derivative / Reachability tube / Robust stability

Funding

None.

Declaration of competing interest

The authors declare that they have no conflict of interest regarding the publication of this article.

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