On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

Open Mathematics

Liu Xianghu¹ 

[1] Department of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006, P. R. China;

关键词: finite approximate controllability;    hilfer fractional derivative;    inequalities;    variational approach;    topological degree approach;    34a08;    34a37;    34c25;   

DOI  :  10.1515/math-2020-0158

来源: DOAJ

【 摘 要 】

The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

【 授权许可】

Unknown