New discussion on nonlocal controllability for fractional evolution system of order 1 < r < 2 $1 < r < 2$

Advances in Difference Equations

Anurag Shukla¹  Shahram Rezapour²  Kottakkaran Sooppy Nisar³  M. Mohan Raja⁴  Velusamy Vijayakumar⁴ 

[1] Department of Applied Sciences, Rajkiya Engineering College Kannauj;Department of Mathematics, Azarbaijan Shahid Madani University;Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University;Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology;

关键词: Fractional derivative;    Nonlocal controllability;    Mild solutions;    Measure of noncompactness;    Integrodifferential system;    Fixed point theorem;   

DOI  :  10.1186/s13662-021-03630-3

来源: DOAJ

【 摘 要 】

Abstract In this manuscript, we deal with the nonlocal controllability results for the fractional evolution system of 1 < r < 2 $1< r<2$ 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.

【 授权许可】

Unknown