# Regularity for time fractional wave problems

## TL;DR

This paper investigates the regularity and singularity structure of solutions to time fractional wave problems using the Galerkin method, providing theoretical insights into their existence and properties.

## Contribution

It introduces a novel analysis of regularity for time fractional wave equations and establishes the unique existence of weak solutions with detailed regularity estimates.

## Key findings

- Proves the existence and uniqueness of weak solutions.
- Provides regularity estimates revealing singularity structures.
- Enhances understanding of time fractional wave problem solutions.

## Abstract

Using the Galerkin method, we obtain the unique existence of the weak solution to a time fractional wave problem, and establish some regularity estimates which reveal the singularity structure of the weak solution in time.