Department of Exact Sciences and Engineering, Academia Militar, Military Academy 2720-113 Amadora, Portugal. Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.
Manoj Kumar
Department of mathematics, Deshbandhu College, University of Delhi, Delhi-110019, India.
Namrata Arya
DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi-221005, India.
Jaimala Bishnoi
Department of mathematics, Chaudhary Charan Singh University Meerut, Meerut-250001, India.
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.
