Inverse source problem for an equation of mixed parabolic-hyperbolic type with the time fractional derivative in a cylindrical domain

Abstract

This article is devoted to the study of an inverse source problem for a mixed type equation with a fractional diffusion equation in the parabolic part and a wave equation in the hyperbolic part of a cylindrical domain. The solution is obtained in the form of FourierBessel series expansion using an orthogonal set of Bessel functions. The theorems of uniqueness and existence of a solution are proved.

Keywords

• inverse problem
• equation of mixed type
• fourier–bessel series
• mittag–leffler function
• uniqueness and existence