# New discussion on nonlocal controllability for fractional evolution system of order 1<r<2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1 < r < 2$\end{document}

Authors
• 1 Vellore Institute of Technology, Vellore, Tamil Nadu, 632 014, India , Vellore (India)
• 2 Rajkiya Engineering College Kannauj, Kannauj, India , Kannauj (India)
• 3 Prince Sattam bin Abdulaziz University, Wadi Aldawaser, 11991, Saudi Arabia , Wadi Aldawaser (Saudi Arabia)
• 4 Azarbaijan Shahid Madani University, Tabriz, Iran , Tabriz (Iran)
• 5 China Medical University, Taichung, Taiwan , Taichung (Taiwan)
Type
Published Article
Journal
Publisher
Springer International Publishing
Publication Date
Nov 06, 2021
Volume
2021
Issue
1
Identifiers
DOI: 10.1186/s13662-021-03630-3
Source
Springer Nature
Keywords
Disciplines
• Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential E
In this manuscript, we deal with the nonlocal controllability results for the fractional evolution system of 1<r<2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1< r<2$\end{document} in a Banach space. The main results of this article are tested by using fractional calculations, the measure of noncompactness, cosine families, Mainardi’s Wright-type function, and fixed point techniques. First, we investigate the controllability results of a mild solution for the fractional evolution system with nonlocal conditions using the Mönch fixed point theorem. Furthermore, we develop the nonlocal controllability results for fractional integrodifferential evolution system by applying the Banach fixed point theorem. Finally, an application is presented for drawing the theory of the main results.