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 ...

We obtain a 3-fold Selberg integral formula. As a consequence we are able to compute the explicit value of the sharp constant in a trilinear fractional integral inequality due to Beckner.

This paper deals with the design of Fractional Order Proportional Integral (FO-PI) controller for the speed control of DC motor. A mathematical model of DC motor control system is derived and based on this model fractional order PI controller is designed using stability boundary locus method to satisfy required gain margin (GM) and phase margin (PM) of the system. Servo and Regulatory tracking ...

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the timeand space-fractional diffusion equation with the quotient of the orders of the timeand space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then ...

In this study, the usefulness of a fractional order PID (proportional plus integral plus derivative)-type controller is investigated on the control of an electromechanical control actuation system. In this extent, the mathematical model of an electromechanically-actuated control actuation system considered is obtained in the continuous time domain first and then a control system with an integer...