In this paper a novel Hybrid Differential Artificial Bee Colony Algorithm (HDABCA) has been proposed for designing a fractional order proportional-integral (FO-PI) speed controller in a Permanent Magnet Synchronous Motor (PMSM) drive. FO-PI controllers’ parameters involve proportionality constant, integral constant and integral order, and hence its design is more complex than that of the usual ...

In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the heavy tailedness of the log returns of the stock prices to be also accounted for in addition to the long range dependence introduced by the fractional Brown...

Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...

The metric polytope ,//~. is defined by the triangle inequalities: xij-Xik-Xjk <~ 0 and xii + Xik + Xjk ~< 2 for all triples i,j, k of(1 ..... n}. The integral vertices of ~¢¢~. are the incidence vectors of the cuts of the complete graph Kn. Therefore, ~¢~. is a relaxation of the cut polytope of K~. We study here the fractional vertices of ~¢¢~. Many of them are constructed from graphs; this is...

In this paper we established the condition for a curve to satisfy stochastic generalized fractional HP (Hamilton-Pontryagin) equations. These equations are described using Itô integral. We have also considered the case of stochastic generalized fractional Hamiltonian equations, for a hyperregular Lagrange function. From the stochastic generalized fractional Hamiltonian equations, Langevin gener...

Abstract. Fractional Lévy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The f...

As an extension of the fact that a sectorial operator can determine an analytic semigroup, we first show that a sectorial operator can determine a real analytic α-order fractional resolvent which is defined in terms of MittagLeffler function and the curve integral. Then we give some properties of real analytic α-order fractional resolvent. Finally, based on these properties, we discuss the regu...

A weighted summation of Integral of Time Multiplied Absolute Error (ITAE) and Integral of Squared Controller Output (ISCO) minimization based time domain optimal tuning of fractional-order (FO) PID or PIλDμ controller is proposed in this paper with a Linear Quadratic Regulator (LQR) based technique that minimizes the change in trajectories of the state variables and the control signal. A class ...

Particle swarm optimization (PSO) is extensively used for real parameter optimization in diverse fields of study. This paper describes an application of PSO to the problem of designing a fractional-order proportional-integral-derivative (PID) controller whose parameters comprise proportionality constant, integral constant, derivative constant, integral order (λ) and derivative order (δ). The pr...

In this paper, we discuss the steady state Fractional Advection Dispersion Equation (FADE) on bounded domains in IRd . Fractional differential and integral operators are defined and analyzed. Appropriate fractional derivative spaces are defined, and shown to be equivalent to the fractional dimensional Sobolev spaces. A theoretical framework for the variational solution of the steady state FADE ...