An inverse problem for the differential operator on the graph with a cycle with different orders on different edges

TL;DR

This paper addresses an inverse spectral problem for a variable order differential operator on a cyclic graph, establishing uniqueness and providing a constructive solution method.

Contribution

It introduces a novel inverse spectral problem for variable order operators on graphs with cycles, including a proof of uniqueness and a constructive solution approach.

Findings

Proved a uniqueness theorem for the inverse spectral problem.

Developed a constructive procedure to solve the inverse problem.

Extended inverse spectral theory to variable order differential operators on cyclic graphs.

Abstract

We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive procedure for the solution of the inverse problem.