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Non-instantaneous Impulsive Riemann-Liouville Fractional Differential Systems: Existence and Controllability Analysis in Banach Spaces
  • Lavina Sahijwani,
  • Sukavanam Nagarajan,
  • Abdul Haq
Lavina Sahijwani
IIT Roorkee

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Sukavanam Nagarajan
Indian Institute of Technology Roorkee
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Abdul Haq
SRM Institute of Science and Technology
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The article is dedicated towards the study of fractional-order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions in Banach spaces. First, mild solution of the system is constructed and subsequently, its existence is proven using Banach's fixed point theorem. Then, results of approximate controllability are established using the concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out corrections in examples presented in previous articles.
23 Apr 2022Submitted to Mathematical Methods in the Applied Sciences
27 Apr 2022Submission Checks Completed
27 Apr 2022Assigned to Editor
02 May 2022Reviewer(s) Assigned
29 Dec 2022Review(s) Completed, Editorial Evaluation Pending
13 Jan 2023Editorial Decision: Revise Major
06 Feb 20231st Revision Received
07 Feb 2023Assigned to Editor
07 Feb 2023Submission Checks Completed
07 Feb 2023Review(s) Completed, Editorial Evaluation Pending
07 Feb 2023Reviewer(s) Assigned
30 Mar 2023Editorial Decision: Revise Minor
31 Mar 20232nd Revision Received
03 Apr 2023Submission Checks Completed
03 Apr 2023Assigned to Editor
03 Apr 2023Review(s) Completed, Editorial Evaluation Pending
05 Apr 2023Reviewer(s) Assigned
11 Apr 2023Editorial Decision: Accept