Controllability For Fractional Differential Systems

In recent years,because fractional-order evolution equations can better describe the actual state of physical and chemical problems than integer-order equations,the role they play in control theory has become increasingly important.This paper mainly studies the precise controllability of the Atangana-Baleanu Caputo fractional order evolution equation and the approximate controllability of the Hilfer fractional order neutral evolution equation.In chapter 3,we use the generalized Grownwall inequality to obtain the relative compactness of the set of mild solutions,and then use Arzela-Ascoli theorem to obtain the precise controllability of the research system.In chapter 4,in the case of strongly continuous semigroups,some relevant assumptions are given,by using the fixed point theorems and sequence approximation under these assumptions The approximate controllability of the research system can be derived.