Chaotic and hypercyclic dynamics in the solution semigroup of a spatial conformable PDE

Abstract

The aim of this study is to analyze the dynamics of an initial value problem associated with a conformable spatial partial differential equation within the space [Formula: see text]. First, we demonstrate that the solution generates a strongly continuous semigroup on [Formula: see text]. Next, we construct a quasiconjugacy between this solution and another semigroup defined on a conformable weighted function space. Under specific conditions, we demonstrate that the problem exhibits both hypercyclicity and chaos.