Initial-boundary value problem for a time-fractional subdiffusion equation on the torus

TL;DR

This paper studies a time-fractional subdiffusion equation on an N-dimensional torus, proving existence and uniqueness of solutions using Fourier methods, with less restrictive initial condition requirements than previous Caputo derivative-based studies.

Contribution

It establishes the existence and uniqueness of classical solutions for a fractional subdiffusion equation on the torus, with improved initial condition criteria.

Findings

Proved existence and uniqueness of solutions.

Derived less restrictive initial condition criteria.

Ensured Fourier series convergence for solutions.

Abstract

An initial-boundary value problem for a time-fractional subdiffusion equation with the Riemann-Liouville derivatives on N-dimensional torus is considered. The uniqueness and existence of the classical solution of the posed problem are proved by the classical Fourier method. Sufficient conditions for the initial function and for the right-hand side of the equation are indicated, under which the corresponding Fourier series converges absolutely and uniformly. It should be noted, that the condition on the initial function found in this paper is less restrictive than the analogous condition in the case of an equation with derivatives in the sense of Caputo