Inverse Problems for Systems of Variable Order Differential Equations with Singularities on Spatial Networks

TL;DR

This paper studies inverse spectral problems for variable order differential equations with singularities on spatial networks, establishing spectral properties and solutions for the inverse problem.

Contribution

It introduces methods to analyze inverse spectral problems for variable order differential equations with singularities on networks, a novel extension in the field.

Findings

Spectral properties of variable order differential equations are characterized.

A solution to the inverse spectral problem is provided.

The approach handles non-integrable singularities on networks.

Abstract

Variable order differential equations with non-integrable singularities are considered on spatial networks. Properties of the spectrum are established, and the solution of the inverse spectral problem is obtained.