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On a study of Sobolev type fractional functional evolution equations
  • Ismail T. Huseynov,
  • Arzu Ahmadova,
  • Nazim Mahmudov
Ismail T. Huseynov
Eastern Mediterranean University

Corresponding Author:ismail.huseynov@emu.edu.tr

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Arzu Ahmadova
Eastern Mediterranean University
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Nazim Mahmudov
Eastern Mediterranean University
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Abstract

Sobolev type fractional functional evolution equations have many applications in the modeling of many physical processes. Therefore, we investigate fractional-order time-delay evolution equation of Sobolev type with multi-orders in a Banach space and introduce an analytical representation of a mild solution via a new delayed Mittag-Leffler type function which is generated by linear bounded operators. Furthermore, we derive an exact analytical representation of solutions for multi-dimensional fractional functional dynamical systems with nonpermutable and permutable matrices. We also study stability analysis of the given time-delay system in Ulam-Hyers sense with the help of Laplace transform.
24 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
25 Feb 2021Submission Checks Completed
25 Feb 2021Assigned to Editor
13 Mar 2021Reviewer(s) Assigned
22 Jun 2021Review(s) Completed, Editorial Evaluation Pending
25 Jun 2021Editorial Decision: Revise Major
26 Aug 20211st Revision Received
27 Aug 2021Submission Checks Completed
27 Aug 2021Assigned to Editor
27 Aug 2021Reviewer(s) Assigned
23 Nov 2021Review(s) Completed, Editorial Evaluation Pending
08 Dec 2021Editorial Decision: Accept
Jun 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 9 on pages 5002-5042. 10.1002/mma.8090