Article

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

Farrukh DekhkonovDepartment of Mathematics Namangan State University Namangan UzbekistanWenke LiCollege of Power and Energy Engineering Harbin Engineering University Harbin ChinaWeipeng WuHarbin Institute of Information Technology Harbin China

Mathematical Methods in the Applied Sciencesjournal2025en

ABI

Abstract

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.

Topics

Stability and Controllability of Differential Equations Differential Equations and Boundary Problems Differential Equations and Numerical Methods

Identifiers

DOI: 10.1002/mma.70223

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