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Approximate controllability of time varying measure differential problem of second order with state-dependent delay and non-instantaneous impulse
  • Surendra Kumar
Surendra Kumar
University of Delhi Faculty of Science

Corresponding Author:[email protected]

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It is comprehended that the systems without any limitation on their Zeno action are enthralled in a vast class of hybrid systems. This article is influenced by a new category of non-autonomous second order measure differential problems with state-dependent delay (SDD) and non-instantaneous impulse (NII). Some new sufficient postulates are created that guarantee solvability and approximate controllability. We employ the fixed point strategy and theory of Lebesgue–Stieltjes integral in the space of piecewise regulated functions. The measure of non-compactness is applied to establish the existence of a solution. Moreover, the measured differential equations generalize the ordinary impulsive differential equations. Thus, our findings are more prevalent than that encountered in the literature. At last, an example is comprised that exhibits the significance of the developed theory.
21 Jun 2022Submitted to Mathematical Methods in the Applied Sciences
22 Jun 2022Submission Checks Completed
22 Jun 2022Assigned to Editor
27 Jun 2022Reviewer(s) Assigned
07 Oct 2022Review(s) Completed, Editorial Evaluation Pending
07 Mar 2023Editorial Decision: Revise Minor
28 Jun 20231st Revision Received
03 Jul 2023Assigned to Editor
03 Jul 2023Submission Checks Completed
03 Jul 2023Review(s) Completed, Editorial Evaluation Pending
03 Jul 2023Reviewer(s) Assigned
11 Aug 2023Editorial Decision: Revise Minor
14 Aug 20232nd Revision Received
14 Aug 2023Assigned to Editor
14 Aug 2023Submission Checks Completed
14 Aug 2023Review(s) Completed, Editorial Evaluation Pending
16 Aug 2023Editorial Decision: Accept