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APPLICATIONS OF FRACTIONAL CALCULUS IN EQUIAFFINE GEOMETRY: PLANE CURVES WITH FRACTIONAL ORDER
  • Muhittin Aydin,
  • Adela Mihai,
  • Asıf Yokus
Muhittin Aydin
Firat University
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Adela Mihai
Technical University of Civil Engineering of Bucharest
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Asıf Yokus
Fırat University
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Abstract

In this paper, we introduce the notions of equiaffine arclength and curvature with fractional order for a plane curve and compare them with the standard ones. In terms of the equiaffine curvature with fractional order we obtain an equiaffine Frenet formula and then construct an analogue of the Fundamental Theorem. The plane curves of constant equiaffine curvature with fractional-order are classified. Several examples are also illustrated.

Peer review status:ACCEPTED

23 Nov 2020Submitted to Mathematical Methods in the Applied Sciences
24 Nov 2020Submission Checks Completed
24 Nov 2020Assigned to Editor
30 Nov 2020Reviewer(s) Assigned
25 Mar 2021Review(s) Completed, Editorial Evaluation Pending
25 Mar 2021Editorial Decision: Revise Major
19 Apr 20211st Revision Received
19 Apr 2021Submission Checks Completed
19 Apr 2021Assigned to Editor
19 Apr 2021Reviewer(s) Assigned
21 May 2021Review(s) Completed, Editorial Evaluation Pending
24 May 2021Editorial Decision: Accept