# Disjoint distributionally chaotic abstract PDE's

## TL;DR

This paper investigates disjoint distributionally chaotic behavior in abstract PDEs with fractional derivatives in Fréchet spaces, providing theoretical analysis, examples, and applications.

## Contribution

It introduces new analysis of disjoint distributional chaos in fractional PDEs within Fréchet spaces, expanding understanding of chaotic dynamics in such systems.

## Key findings

- Identification of conditions for disjoint distributional chaos in fractional PDEs
- Examples illustrating chaotic behavior in specific PDE models
- Applications demonstrating relevance to real-world systems

## Abstract

In this paper, we analyze disjoint distributionally chaotic abstract non-degenerate partial differential equations in Fr\' echet spaces, with integer or Caputo time-fractional derivatives. We present several illustrative examples and applications of our results established.