On the Regional Controllability for Hadamard-Caputo Fractional Ultra-Slow Diffusion Processes

6 Pages Posted: 12 Nov 2018

See all articles by Ruiyang Cai

Ruiyang Cai

Donghua University

Fudong Ge

China University of Geosciences

Yang Quan Chen

University of California, Merced

Chunhai Kou

Donghua University

Date Written: July 2018

Abstract

In this article, we address the regional controllability problem for ultra-slow diffusion processes governed by Hadamard-Caputo time fractional diffusion systems. Some necessary and sufficient conditions on both regional exact controllability and regional approximate controllability of the considered systems are first obtained. Secondly, we provide a necessary and sufficient condition on the minimum number of the actuators to achieve the regional approximate controllability. Moreover, by applying the Hilbert Uniqueness Method (HUM), the optimal actuators with minimum energy can be chosen among the whole admissible ones. Finally, an example is given to illustrate our results.

Keywords: Hadamard-Caputo Fractional Derivative; Regional Controllability; Hilbert Uniqueness Method; Minimum Energy Control

Suggested Citation

Cai, Ruiyang and Ge, Fudong and Chen, Yang Quan and Kou, Chunhai, On the Regional Controllability for Hadamard-Caputo Fractional Ultra-Slow Diffusion Processes (July 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018. Available at SSRN: https://ssrn.com/abstract=3282725 or http://dx.doi.org/10.2139/ssrn.3282725

Ruiyang Cai

Donghua University ( email )

Shanghai 200051
China

Fudong Ge (Contact Author)

China University of Geosciences ( email )

Wuhan, China
Wuhan, Hubei
China

Yang Quan Chen

University of California, Merced ( email )

P.O. Box 2039
Merced, CA 95344
United States

Chunhai Kou

Donghua University ( email )

Shanghai 200051
China

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