Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients
Analysis of PDEs
2026-04-07 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2604.03739,
title = {Solvability of a Mixed Problem for a Time-Fractional PDE with Time-Space Degenerating Coefficients},
author = {Bakhodirjon Toshtemirov and Azizbek Mamanazarov},
journal= {arXiv preprint arXiv:2604.03739},
year = {2026}
}