On solvability of the non-local problem for the fractional mixed-type equation with Bessel operator

TL;DR

This paper investigates the solvability of a non-local boundary value problem for a mixed-type PDE involving a Bessel operator and fractional derivatives, providing explicit solutions and conditions for uniqueness.

Contribution

It introduces a method to explicitly solve the non-local problem using Fourier-Bessel series and establishes criteria for the problem's unique solvability.

Findings

Explicit solution expressed via Fourier-Bessel series

Connection between data and solvability conditions

Criteria for unique solutions

Abstract

The non-local problem is considered for the partial differential equation of mixed-type with Bessel operator and fractional order. An explicit solution is represented by Fourier-Bessel series in the given domain. It is established the connection between the given data and the unique solvability of the problem.