Time‐Optimal Control Problem for the Heat Equation With Fractional Caputo Derivative

ABSTRACT 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.

Hali tarjima qilinmagan