Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients

TL;DR

This paper proves the unique solvability of a mixed boundary value problem for a fractional PDE with degenerating coefficients, revealing spectral properties and the influence of degeneracy on fractional diffusion.

Contribution

Introduces a new operator and spectral analysis method to establish solvability and spectral properties of a degenerate fractional PDE.

Findings

Existence of eigenvalues and eigenfunctions for the spectral problem.

Operator has a discrete spectrum.

Degeneracy affects the solvability of fractional diffusion processes.

Abstract

In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation of variables, we establish the existence of eigenvalues and eigenfunctions for the associated spectral problem and prove that the operator possesses a discrete spectrum. Additionally, we establish the relationship between the given data and the unique solvability of the problem, offering new insights into how degeneracy influences fractional diffusion processes.