The time-fractional Airy equation on the metric graphs

TL;DR

This paper studies the time-fractional Airy equation on metric graphs, analyzing solutions, properties of potentials, and proving uniqueness using inequalities and estimates.

Contribution

It introduces analysis of the time-fractional Airy equation on graphs with new solution methods and uniqueness proofs.

Findings

Solutions for the time-fractional Airy equation on graphs are constructed.

Properties of potentials for this equation are characterized.

Uniqueness of solutions is established using Grönwall-Bellman inequality.

Abstract

In this work we investigate Cauchy problem and initial boundary value problem for time-fractional Airy equation on the graphs with infinite and finite bonds. We studied properties of potentials for this equation and using these properties found the solutions of the considered problems. The uniqueness theorem is proved using the analogue of Gr\"onwall-Bellman inequality and a-priory estimate.