Shandong Science ›› 2020, Vol. 33 ›› Issue (6): 110-117.doi: 10.3976/j.issn.1002-4026.2020.06.015

• Other Research Article • Previous Articles     Next Articles

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

WANG Xing-zhao,GU Hai-bo*   

  1. School of Mathematics Sciences, Xinjiang Normal University, Urumqi 830017, China
  • Online:2020-12-09 Published:2020-12-11

Abstract: 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.

Key words: Hilfer fractional derivative, evolution equation, nonlocal conditions, mild solution, partialapproximate controllability

CLC Number: 

  • O175.2