# Blowing-up solutions of the time-fractional dispersive equations

## TL;DR

This paper investigates finite-time blow-up phenomena for various time-fractional dispersive equations on bounded domains, providing sufficient conditions and analyzing the effects of non-linearity and maximum principles.

## Contribution

It introduces new blow-up criteria for time-fractional dispersive equations and examines the impact of gradient non-linearity on global solutions.

## Key findings

- Sufficient conditions for finite-time blow-up are established.
- Maximum principle and non-linearity effects are analyzed.
- Illustrative examples demonstrate theoretical results.

## Abstract

This paper is devoted to the study of initial-boundary value problems for time-fractional analogues of Korteweg-de Vries, Benjamin-Bona-Mahony, Burgers, Rosenau, Camassa-Holm, Degasperis-Procesi, Ostrovsky and time-fractional modified Korteweg-de Vries-Burgers equations on a bounded domain. Sufficient conditions for the blowing-up of solutions in finite time of aforementioned equations are presented. We also discuss the maximum principle and influence of gradient non-linearity on the global solvability of initial-boundary value problems for the time-fractional Burgers equation. The main tool of our study is the Pohozhaev nonlinear capacity method. We also provide some illustrative examples.