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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
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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.

Peer review status:UNDER REVIEW

24 Feb 2021Submitted to Mathematical Methods in the Applied Sciences
25 Feb 2021Assigned to Editor
25 Feb 2021Submission Checks Completed
13 Mar 2021Reviewer(s) Assigned