Actuator characterisations to achieve approximate controllability for a class of fractional sub-diffusion equations

ABSTRACT

This paper is devoted to analysing the actuator characterisations for the fractional sub-diffusion equation under consideration to become approximately controllable. Two different cases are considered, where the control inputs emerge in the differential equation as distributed inputs and as boundary inputs in the boundary conditions. The dual system for fractional sub-diffusion equation is solved and the necessary and sufficient conditions for the approximate controllability of the system are established. Several examples are worked out in the end to illustrate our results.

KEYWORDS:

• Approximate controllability
• sub-diffusion process
• fractional order
• distributed inputs
• boundary inputs

Acknowledgements

This work was supported by Chinese Universities Scientific Fund No.CUSF-DH-D-2014061 and the Natural Science Foundation of Shanghai (no. 15ZR1400800).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Chinese Universities Scientific Fund No.CUSF-DH-D-2014061 and the Natural Science Foundation of Shanghai [no. 15ZR1400800].