In this paper, firstly, new Hermite–Hadamard type inequalities for harmonically convex functions in fractional integral forms are given. Secondly, Hermite–Hadamard–Fejer inequalities for harmonically convex functions in fractional integral forms are built. Finally, an integral identity and some Hermite–Hadamard–Fejer type integral inequalities for harmonically convex functions in fractional integral forms are obtained. Some results presented here provide extensions of others given in earlier works.

Conformable fractional derivative is introduced by the authors Khalil at al in 2014. In this study, we investigate the frenet frame with respect to conformable fractional derivative. Curvature and torsion of a conformable curve are defined and the geometric interpretation of these two functions is studied. Also, fundamental theorem of curves is expressed for the conformable curves and an example of the curve corresponding to a fractional differential equation is given.

Conformable fractional derivative is introduced by the authors Khalil et al. In this study we develop their concept and introduce multi-variable conformable derivative for a vector valued function with several variables

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We consider a first-order infinitesimal bending of a curve in R 3 to obtain a ruled surface. This paper investigates this kind of ruled surfaces and their properties. Also, we obtain conditions for ruled surfaces obtained by bending to be developable.