# Br\"uck Conjecture with hyper-order less than one

## TL;DR

This paper proves Brück's conjecture for functions of hyper-order less than one by analyzing the infinite hyper-order of solutions to a specific complex differential equation.

## Contribution

It confirms Brück's conjecture under the condition of hyper-order less than one, advancing understanding of complex differential equations.

## Key findings

- Brück's conjecture holds for hyper-order less than one
- Solutions exhibit infinite hyper-order under the studied conditions
- Provides new insights into the growth of solutions to complex differential equations

## Abstract

In this paper we affirm Br\"{u}ck conjecture provided $f$ is of hyper-order less than one by studying the infinite hyper-order of solutions of a complex differential equation.