Approximate controllability of impulsive Hilfer fractional differential inclusions


Authors

Jun Du - School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China. - Department of Applied Mathematics, Huainan Normal University, Huainan 232038, P. R. China. Wei Jiang - School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China. Azmat Ullah Khan Niazi - School of Mathematical Sciences, Anhui University, Hefei 230601, P. R. China.


Abstract

In this paper, firstly by utilizing the theory of operators semigroup, probability density functions via impulsive conditions, we establish a new \(PC_{1-\nu}\)-mild solution for impulsive Hilfer fractional differential inclusions. Secondly we prove the existence of mild solutions for the impulsive Hilfer fractional differential inclusions by using fractional calculus, multi-valued analysis and the fixed-point technique. Then under some assumptions, the approximate controllability of associated system are formulated and proved. An example is provided to illustrate the application of the obtained theory


Keywords


MSC


References