On the solution of \(\mathcal{T}-\)controllable abstract fractional differential equations with impulsive effects
Author
Ram Gautam, Ganga
Pinelas, Sandra
Kumar, Manoj
Arya, Namrata
Bishnoi, Jaimala
Abstract
In this research article, we delimitate the definition of mild solution for abstract fractional differential equations with state-dependent delay (AFDEw/SDD) of order \(\alpha\in(1,2)\) with impulsive effects and compare the solution to the second-order impulsive differential equations. Further, we obtain sufficient conditions of the existence of mild solution for instantaneous and non-instantaneous impulsive fractional functional differential inclusions with state-dependent delay (IFDIw/SDD) using the multi-valued fixed point theory and operator techniques. Furthermore, we study the trajectory controllability (\(\mathcal{T}-\)controllability) of the AFDEw/SDD. At last, we present some examples to illustrate the sufficient conditions involving partial and ordinary derivatives.