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Ulam's type stabilities for conformable fractional differential equations with delay
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  • Sen Wang,
  • Wei Jiang,
  • Jiale Sheng,
  • Rui Li
Sen Wang
Anhui University
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Wei Jiang
Anhui University
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Jiale Sheng
Anhui University
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Rui Li
Anhui University
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Abstract

In this paper, we investigate the existence and uniqueness of solutions and Ulam's type stabilities including the well-known Ulam-Hyers stability and the newly extended Ulam-Hyers' conformable exponential stability for two classes of fractional differential equations with the conformable fractional derivative and the time delay. The Banach contraction principle, the technique of Picard operator, the Gronwall integral inequalities and generalized iterated integral inequality in the sense of conformable fractional integral are the main tools for deriving our main results. Finally, several illustrative examples will be presented to demonstrate our work.

Peer review status:UNDER REVIEW

28 Oct 2020Submitted to Mathematical Methods in the Applied Sciences
05 Nov 2020Submission Checks Completed
05 Nov 2020Assigned to Editor
17 Nov 2020Reviewer(s) Assigned
25 Feb 2021Review(s) Completed, Editorial Evaluation Pending
27 Feb 2021Editorial Decision: Revise Major
11 Mar 20211st Revision Received
11 Mar 2021Submission Checks Completed
11 Mar 2021Assigned to Editor
13 Mar 2021Reviewer(s) Assigned