Nonlocal problem with conjugation conditions for a degenerate higher order equations with the Caputo fractional derivative

TL;DR

This paper investigates a nonlocal boundary value problem for a degenerate higher-order fractional differential equation with Caputo derivatives, providing a solution construction via Fourier series and establishing conditions for uniqueness.

Contribution

It introduces a novel approach to solving nonlocal problems with conjugation conditions for degenerate fractional equations using Fourier series methods.

Findings

Solution constructed using Fourier series in eigenfunctions

Uniqueness criterion for solutions established

Analysis applicable to degenerate higher-order fractional equations

Abstract

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