# Singularity formation in fractional Burgers' equations

## TL;DR

This paper investigates finite-time singularity formation in fractional Burgers' equations, providing proofs, mechanisms, and estimates, and explores their application to modeling job market dynamics.

## Contribution

It offers the first detailed analysis of singularity formation in fractional Burgers' equations and connects these findings to real-world job market modeling.

## Key findings

- Finite time singularities are proven to occur in fractional Burgers' equations.
- The underlying mechanism of singularity formation is elucidated.
- Precise estimates on blow-up time are provided.

## Abstract

The formation of singularities in finite time in non-local Burgers' equations, with time-fractional derivative, is studied in detail. The occurrence of finite time singularity is proved, revealing the underlying mechanism, and precise estimates on the blow-up time are provided. The employment of the present equation to model a problem arising in job market is also analyzed.