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Characteristic between species is an important feature of animal investigation and preservation. For turtles, different analysis is possibly respected implements for identification. Shell shape is an essential component of analysis and classification in turtles and can be simply styled and measured by conformal geometric (CG). Here, we focus on the shell shape of a Southeast Asian leaf turtle by utilizing CG approaches. CG approaches recognized important differences in shell shape of turtles by using the convexity part of the shell structure. The symmetry of the sail shape in this type of turtles is a very important recognition. Therefore, we introduce a symmetric differential operator using its roots to study the shell shape. 2D printing tool paths are recognized for these shells. Keywords: Conformal geometry, fractional differential operator, shell morphology, fractional calculus, analytic function, unit disk, fractional entropy