On a problem with conjugation conditions for an equation of even order with a fractional derivative in the sense of Caputo

TL;DR

This paper investigates a high-order fractional differential equation with conjugation conditions, establishing a uniqueness criterion and constructing solutions via Fourier series in a rectangular domain.

Contribution

It introduces a new approach to solving high-order fractional equations with conjugation conditions, including a criterion for solution uniqueness.

Findings

Established a uniqueness criterion for the problem.

Constructed solutions using Fourier series in eigenfunctions.

Analyzed the conjugation conditions for fractional differential equations.

Abstract

In this work, for an equation of high even order with a fractional derivative in the sense of Caputo, a problem is studied in a rectangular domain with conjugation conditions. A criterion for the uniqueness of a solution is given. The solution is constructed in the form of a Fourier series in the eigenfunctions of a one-dimensional problem.