一类具有非局部条件的Sobolev型Hilfer分数阶发展方程的偏近似可控性

Partially approximate controllability of Sobolev-Type Hilfer fractional evolution equations with nonlocal conditions

研究了Hilbert空间中具有非局部条件的Sobolev型Hilfer分数阶发展方程的偏近似可控性。通过使用变分法和近似法,构造了控制系统的近似解算子并得到了近似解集的紧性。在非局部函数不满足Lipschitz条件的情况下,得到了控制系统偏近似可控的充分条件。

In this paper,we study partially approximate controllability of Sobolev-type Hilfer fractional evolution equations with nonlocal conditions in Hilbert spaces.Using variational approach and approximating method,we provide the approximate solution operator of the control system and obtain the compactness of the approximate solution set.The sufficient conditions for the partially approximate controllability of the control system are obtained when Lipschitz conditions for the nonlocal function are not met.