31 www.erpublication.org  Abstract—In order to overcome the nonlinear characteristics of permanent magnet synchronous motor (PMSM), fractional order (FO) fuzzy proportional integral (PI) controller was designed based on the fractional order calculus and fuzzy technology for PMSM with the nonlinearity and time-varying parameters at work. Fuzzy control rules are designed in the light of running ...

This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.

In the present article, a comprehensive review of relevant literature is presented to highlight the role of fractional calculus in the field of thermoelasticity. This review is devoted to the generalizations of the classical heat conduction equation and formulation of associated theories of fractional thermoelasticity. The recently developed fractional order thermoelastic models are described w...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

The fractional order calculus theory and its modeling methods have been applied widely in control field. And design of fractional order control systems become hot point of recent years. This paper establishes fractional order systems which parameters are obtained by Bode’s ideal transfer function method to get the desired frequency response. Apply this method a new control structure of fraction...

Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noetherlike theorem to the more general context of the fractional optimal control. As a corollary, it follows that in the fractional case the autonomous Hamiltonian does not define...

Abstract The research of a formulation to model non-local interactions in the mechanical behavior matter is currently an open problem. In this context, strong based on fractional calculus provided paper. This derived from analogy with long-memory viscoelastic models. Specifically, same kind power-law time-dependent kernel used Boltzmann integral stress-strain relation as Fredholm relation. lead...

Firstly the one-dimension digital fractional order SavitzkyGolay differentiator (1-D DFOSGD), which generalizes the Savitzky-Golay filter from the integer order to the fractional order, is proposed to estimate the fractional order derivative of the noisy signal. The polynomial least square fitting technology and the Riemann-Liouville fractional order derivative definition are used to ensure rob...