The Method of Potentials for the Airy Equation of Fractional Order

TL;DR

This paper develops a method based on potentials to solve initial-boundary value problems for the time-fractional Airy equation, establishing solution properties, uniqueness, and estimates.

Contribution

It introduces a potential-based approach for the fractional Airy equation and proves solution uniqueness and estimates using new analytical techniques.

Findings

Constructed solutions for fractional Airy equation boundary problems

Proved uniqueness of solutions using an analogue of Gronwall-Bellman inequality

Established a priori estimates for solutions

Abstract

In this work, initial-boundary value problems for the time-fractional Airy equation are considered on different intervals. We study the properties of potentials for this equation and, using these properties, construct solutions to the considered problems. The uniqueness of the solution is proved using an analogue of the Gronwall-Bellman inequality and an a priori estimate.