An extension of the general fractional calculus (GFC) an arbitrary order, proposed by Luchko, is formulated. This also based on a multi-kernel approach, in which Laplace convolutions different Sonin kernels are used. The GFC order considered for case intervals (a,b) where ??<a<b??. Examples operators orders proposed.

The aim of this paper is to design a Fractional Order Sliding Mode Controllers (FOSMC)for a class of DC-DC converters such as boost and buck converters. Firstly, the control lawis designed with respect to the properties of fractional calculus, the design yields an equiv-alent control term with an addition of discontinuous (attractive) control law. Secondly, themathematical proof of the stabilit...

In this paper, a new approach to stability for fractional order control system is proposed. Here a dynamic system whose behavior can be modeled by means of differential equations involving fractional derivatives. Applying Laplace transforms to such equations, and assuming zero initial conditions, causes transfer functions with no integer powers of the Laplace transform variable s to appear. In ...

In this work, we recall some definitions on fractional calculus with discrete-time. Then, introduce a discrete-time Hopfield neural network (D.T.H.N.N) non-commensurate variable-order (V.O) for three neurons. After that, phase-plot portraits, bifurcation and Lyapunov exponents diagrams are employed to verify that the proposed discrete time variable order has chaotic behavior. Furthermore, use 0...

Recently, interest in fractional-order inductors (FOIs) has increased since they allow for accurate and robust models of dynamical systems to be designed. However, practical implementation these not been possible due the lack single FOI realizations. To address this challenge, work, we propose a simple-to-realize inductor design with variable constant phase angle (CPA). The relies on characteri...

This paper is concerned with behavior analysis and improvement of wind turbines with Doubly Fed Induction Generator (DFIG) when using a new fractional-order control strategy during wind variations. A doubly fed induction generator, two types of variable frequency power electronic converters and two input wind waveforms are considered. A fractional-order control strategy is proposed for the wind...

Fractional calculus; Conformable operators; Calculus on time scales Abstract A conformable time-scale fractional calculus of order a 2 0; 1 is introduced. The basic tools for fractional differentiation and fractional integration are then developed. The Hilger timescale calculus is obtained as a particular case, by choosing a 1⁄4 1. a 2015 The Authors. Production and hosting by Elsevier B.V. on ...