Inverse problem of determining time-dependent leading coefficient in the time-fractional heat equation

Serikbaev D. Ruzhansky M. Tokmagambetov N.
December 2025 Springer Nature

Fractional Calculus and Applied Analysis
2025 #28 Issue 6 2918 - 2968 pp.

This paper delves into the exploration of direct and inverse problems pertaining to the time-fractional heat equation featuring a time-dependent leading coefficient for positive operators. Initially, we address the direct problem, where we establish the unique existence of the generalized solution and derive various regularity results. Subsequently, we focus on the inverse problem aimed at determining the leading coefficient. Through the utilization of insights gleaned from the direct problem, we demonstrate the Lipschitz stability result for this inverse problem.

Caputo fractional derivative , Coefficient inverse problem , Direct problem , Heat equation , Positive operator , Well-posedness

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom

Institute of Mathematics and Mathematical Modeling
Department of Mathematics: Analysis
School of Mathematical Sciences

10 лет помогаем публиковать статьи Международный издатель

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