Regional Controllability for Caputo Type Semi-Linear Time-Fractional Systems

Abstract

The main purpose of this paper, is to study the regional controllability concept of a semi-linear time-fractional diffusion systems involving Caputo derivative of order α ∈ (0, 1). The main result is obtained by using an extension of the Hilbert Uniqueness Method (HUM) in addition to a fixed point technique and under several assumptions on the data of the considered equation. At the end, some numerical simulations are given to illustrate the efficiently of our result.

Keywords

• regional controllability
• fractional calculus
• caputo time-fractional systems
• fixed point theorems
• hum approach
• compact operators