Approximate controllability of fractional differential equations driven by Markovian switching and Lévy noise with infinite delay

Abstract

Motivated by applications of nonlinear dynamical systems and based on some existing works, we introduce a general class of Atangana-Baleanu nonlinear fractional neutral differential equations driven by Markovian switching and Lévy noise with infinite delay. In this paper, we aim to derive new results on the existence of solutions as well as approximate controllability for the corresponding Atangana-Baleanu equations in Banach spaces. Under suitable conditions with the help of semigroup theory, fixed point theorem as well as stopping time argument, we prove the main results. As an application, we present two examples with numerical simulations to support our theory. The results obtained in this paper improve and extend some related conclusions on this topic.