Inverse source problem for the space-time fractional parabolic equation on a metric star graph with an integral overdetermination condition

TL;DR

This paper studies the inverse source problem for a space-time fractional parabolic equation on a star graph, establishing existence, uniqueness, and the well-posedness of the inverse problem using operator theory.

Contribution

It introduces the first analysis of an inverse source problem with integral overdetermination for fractional parabolic equations on star graphs.

Findings

Proved existence and uniqueness of strong solutions.

Established the well-defined nature of the resolvent operator.

Extended inverse problem analysis to fractional derivatives on metric graphs.

Abstract

In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are proved with the classical functional method based on a priori estimates. Moreover, the inverse source problem with the integral overdetermination condition for space-time fractional derivatives in Sobolev spaces is first considered in the present paper. By transforming the inverse problem to the operator-based equation, we showed that the corresponding resolvent operator is well-defined.