Special Fractional Curve Pairs with Fractional Calculus

Abstract

In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curve pairs is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Conformable fractional derivative that fits the algebraic structure of differential geometry derivative is used. This effect is examined with the help of examples consistent with the theory and visualized for different values of the Conformable fractional derivative. The difference of this study from others is the use of Conformable fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics,signal processing, etc. Fractional derivatives and integrals have become an extremely important and new mathematical method in solving various problems in many sciences.

C α −ruled surfaces respect to direction curve in fractional differential geometry

“…( 31), ( 33), ( 34) and ( 35) are considered together with Eqs. ( 9), ( 10) and (11), the C α −coefficients of the C α −second fundamental form, can be seen as follows…”

“…Gozutok U. et al are analyzed the basic concepts of curves and Frenet frame in fractional order with the help of conformable local fractional derivative [8]. On the other hand Has A. and Yılmaz B. are investigated some special curves and curve pairs in fractional order with the help of conformable Frenet frame [11,12]. In addition, electromagnetic fields and magnetic curves are investigated under fractional derivative by Has A. and Yılmaz B.…”

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

“…For instance, Gozutok U. et al are reconstructed the Frenet frame, which is the most commonly used structure in characterizing curves, using the conformable derivative [15]. Furthermore, Has A. and Yilmaz B. are conducted in-depth studies on curves and surfaces [16][17][18][19]31]. These research works demonstrate that fractional calculus provides a different perspective in the field of geometry and that the conformable derivative is a more effective tool for understanding and characterizing the geometrical structures in fractional analyses.…”

Fractional approach to evolution of the magnetic field lines near the magnetic null points

“…This approach is given by milici and Machado, [34]. In [35,36], Has et al investigated the many special curves by using conformable fractional derivatives. Electromagnetic curves and some special magnetic curves with the help of fractional derivatives, [37][38][39].…”