Remarks on the controllability of fractional differential equations

Abstract

In this paper, we study the approximate controllability of a linear fractional differential equation by using the method of regularization of Tikhonov. New concepts and results about controllability are established. Then, under the condition of the positivity of the controllability operator, we obtain that the linear system can be steered to an arbitrary small neighbourhood of the fractional integral of the state at final time.

Keywords:

• fractional Caputo derivatives
• fractional differential equations
• mild solution
• approximate controllability
• optimal controls
• regularization of  Tikhonov

AMS Subject Classifications:

• 34K37
• 47A10
• 49J15

Notes

This work was supported by the NSF of China [grant number 11001034].