This study reveals the minimal time to reach desired average temperature in a domain using fractional calculus and control methods.
This paper addresses a time‐optimal control problem for the heat equation involving a Caputo fractional derivative. The control function is applied on a specific portion of the domain boundary. The main objective is to determine the minimal time required to achieve a prescribed average temperature within the domain. By employing spectral methods and properties of the Mittag–Leffler function, we derive an explicit estimate for the minimal time under suitable conditions.
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Dekhkonov et al. (2025) studied this question.
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