Approximate controllability of impulsive fractional evolution equations of order 1<α<2$$ 1&amp;amp;amp;lt;\alpha &amp;amp;amp;lt;2 $$ with state‐dependent delay in Banach spaces. (12th July 2022)

• Record Type: Journal Article
• Authors: Arora, Sumit; Mohan, Manil T.; Dabas, Jaydev
• Is Part Of: Mathematical methods in the applied sciences. Volume 46:Number 1(2023)
• Page Start: 531
• Page End: 559
• Publication Date: 2022-07-12
• Subjects: approximate controllability -- fractional derivative -- Mainardi's Wright‐type function -- noninstantaneous impulses -- state‐dependent delay; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.8527
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This article deals with the approximate controllability problem for fractional evolution equations involving noninstantaneous impulses and state‐dependent delay. In order to derive sufficient conditions for the approximate controllability of our problem, we first consider the linear‐regulator problem and find the optimal control in the feedback form. By using this optimal control, we develop the approximate controllability of the linear fractional control system. Further, we obtain sufficient conditions for the approximate controllability of the nonlinear problem. In the end, we provide a concrete example to support the applicability of the derived results.