Recently, fractional calculus has attracted much attention since it plays an important role in many fields of science and engineering. Especially, the study on stability of fractional differential equations appears to be very important. In this paper, a brief overview on the recent stability results of fractional differential equations and the analytical methods used are provided. These equatio...

Chaos synchronization of coupled fractional order differential equation is receiving increasing attention because of its potential applications in secure communications and control processing. The aim of this paper is synchronization between two identical or different delay fractional-order chaotic systems in finite time. At first, the predictor-corrector method is used to obtain the solutions ...

Fractional calculus is closer to reality and has the same memory characteristics as memristor. Therefore, a fractional-order multistable locally active memristor proposed for first time in this paper, which infinitely many coexisting pinched hysteresis loops under different initial states wide regions. Through theoretical numerical analysis, it found that stronger wider nonvolatile ranges than ...

An important class of fractional differential and integral operators is given by the theory calculus with respect to functions, sometimes called ?-fractional calculus. The operational approach has proved useful for understanding extending this topic study. Motivated equations, we present an Laplace transforms functions their relationship functions. This makes generalised much easier analyse app...

In this work, a new control scheme for synchronization of AC microgrids with upstream power grid is presented. The effects of V2Gs (vehicle to grid) dynamics on synchronization process is studied. This new control approach is based on the optimal fractional calculus and has been developed for synchronization of the microgrid. The V2Gs effect on the dynamics of the microgrid is analyzed through ...

for any $k in mathbb{n}$, the $k$-subdivision of graph $g$ is a simple graph $g^{frac{1}{k}}$, which is constructed by replacing each edge of $g$ with a path of length $k$. in [moharram n. iradmusa, on colorings of graph fractional powers, discrete math., (310) 2010, no. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $g$ has been introduced as a fractional power of $g$, denoted by ...

FRACTIONAL calculus has been applied in all MAD (modeling, analysis and design) aspects of control systems engineering since Shunji Manabe’s pioneering work in early 1960s. The 2016 International Conference on Fractional Differentiation and Its Applications (ICFDA) was held in Novi Sad, Serbia, July 18-20. Quoting from the website http://www.icfda16.com/ “Fractional Calculus (FC for short) is a...

The investigation in the present paper is to obtain certain types of relations for the well known hypergeometric functions by employing the technique of fractional derivative and integral. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C20, 26A33. Keywords—Fractional Derivatives and Integrals, Hypergeometric functions. THE names fractional calculus is concerned with the ge...