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...

Starting with the problem of connecting photovoltaic (PV) system to main grid, this article presents control a grid-connected PV using fractional-order (FO) sliding mode (SMC) and FO-synergetic controllers. The mathematical model connected grid together chain intermediate elements their systems. To obtain superior performance, robustness performance an SMC-type controller for udc voltage in DC ...

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.

Images are frequently disrupted by noise of all kinds, making image restoration very challenging. There have been many different denoising models proposed over the last few decades. Some preserve image’s smooth region, while others texture margin. One these methods is using quantum calculus. Quantum calculus a branch mathematics that deals with manipulation functions and operators in mechanical...

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...