Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order r∈(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r} \in (1,2)$$\end{document} via sectorial operator

In this study, we investigate nonlocal problems for a class of the Sobolev type fractional delay impulsive integrodifferential inclusions of order r∈(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r} \in (1,2)$$\end{document} via sectorial operator in Hilbert space. The results are obtained by engaging of mixed Volterra-Fredholm integrodifferential systems, sectorial operator of type (P,κ,r,γ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(P,\kappa ,{r},\gamma )$$\end{document} and Martelli’s fixed point theorem under the assumption that the corresponding linear system is approximately controllable. Finally, an example is given to illustrate the effectiveness of the results obtained.