Regional fractional enlarged controllability of Riemann–Liouville fractional time linear systems

Abstract This paper investigates the regional fractional enlarged controllability of parabolic linear systems governed by Riemann–Liouville fractional time derivatives. The goal is to design a control that, while ensuring the fractional derivative of the system's state satisfies predetermined criteria, steers the system's fractional output to a desired state within a designated subregion of the domain. The optimal control is defined using two separate methods: subdifferential theory and the Lagrangian technique. We establish the prerequisites for achieving regional controllability by employing these methods. Finally, a Uzawa‐type algorithm is developed and used in numerical simulations to validate the theoretical results, demonstrating the practicality of the proposed control in real‐world scenarios.