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\begin{document}

\title{APPLICATIONS OF FRACTIONAL CALCULUS IN EQUIAFFINE GEOMETRY: PLANE CURVES
WITH FRACTIONAL ORDER}



\author[1]{Muhittin Aydin}%
\author[2]{Adela Mihai}%
\author[3]{Asıf Yokus}%
\affil[1]{Firat University}%
\affil[2]{Technical University of Civil Engineering of Bucharest}%
\affil[3]{Fırat University}%


\vspace{-1em}



  
  \date{May 16, 2024}


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\begin{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.%
\end{abstract}%



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