Approximate Controllability for a Class of Semi-Linear Fractional Integro-Differential Impulsive Evolution Equations of Order 1 < α < 2 with Delay

Daliang Zhao ()
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Daliang Zhao: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Mathematics, 2023, vol. 11, issue 19, 1-19

Abstract: This article is mainly concerned with the approximate controllability for some semi-linear fractional integro-differential impulsive evolution equations of order 1 < α < 2 with delay in Banach spaces. Firstly, we study the existence of the P C -mild solution for our objective system via some characteristic solution operators related to the Mainardi’s Wright function. Secondly, by using the spatial decomposition techniques and the range condition of control operator B , some new results of approximate controllability for the fractional delay system with impulsive effects are obtained. The results cover and extend some relevant outcomes in many related papers. The main tools utilized in this paper are the theory of cosine families, fixed-point strategy, and the Grönwall-Bellman inequality. At last, an example is given to demonstrate the effectiveness of our research results.

Keywords: approximate controllability; fractional integro-differential impulsive evolution equation; delay; Schaefer’s fixed point theorem; range condition of control operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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