In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curve pairs investigated. As it known, there are not many studies a geometric interpretation calculus. When examining analysis curve, Conformable derivative that fits algebraic structure differential geometry used. This examined with help examples consistent theory and visualized for differe...

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account general form non-locality in kernels differential and integral operators. Self-consistency involves proving generalizations all fundamental theorems for generalized In the FVC from power-law nonlocality space, we use (GFC) Luchko approach, which was published 2021. This...

Fractional calculus is a generalization of the integration and differentiation to the fractional (non-integer) order. In this paper, for the first time, we devised a fractionalorder adaptive compensation (FO-AC) method for cogging effect minimization for permanent magnetic synchronous motors (PMSM) position and velocity servo system. Cogging effect is a major disadvantage of PMSM. In our FO-AC ...

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.