Forward and Inverse Problems for Subdiffusion Equation with Time-Dependent Coefficients

TL;DR

This paper investigates forward and inverse problems for subdiffusion equations with time-dependent coefficients, establishing uniqueness and existence results using Fourier methods for determining the right-hand side.

Contribution

It provides new theoretical results on the solvability of forward and inverse subdiffusion problems with time-dependent coefficients using classical Fourier analysis.

Findings

Proved uniqueness of solutions for the inverse problem.

Established existence of solutions for the forward problem.

Applied Fourier methods to analyze subdiffusion equations.

Abstract

In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of the uniqueness and existence of forward and inverse problems for determining the right-hand side of the equation are proved.