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

TL;DR

This paper studies direct and inverse problems for a time-fractional heat equation with a time-dependent coefficient, establishing existence, regularity, and uniqueness results using eigenfunction expansion.

Contribution

It introduces a method to determine the time-dependent leading coefficient in a fractional heat equation, proving well-posedness of the inverse problem.

Findings

Unique existence of solutions for the direct problem.

Regularity results for the solutions.

Well-posedness of the inverse coefficient determination.

Abstract

In this paper, we investigate direct and inverse problems for the time-fractional heat equation with a time-dependent leading coefficient for positive operators. First, we consider the direct problem, and the unique existence of the generalized solution is established. We also deduce some regularity results. Here, our proofs are based on the eigenfunction expansion method. Second, we study the inverse problem of determining the leading coefficient, and the well-posedness of this inverse problem is proved.