Fractional calculus is a generalization of the integration and differentiation to the fractional (non-integer) order. In this paper, for the first time, we devised a fractionalorder adaptive compensation (FO-AC) method for cogging effect minimization for permanent magnetic synchronous motors (PMSM) position and velocity servo system. Cogging effect is a major disadvantage of PMSM. In our FO-AC ...

The question about behavior of gaps between zeros polynomials under differentiation is classical and goes back to Marcel Riesz. Recently, Stefan Steinerberger [42] formally derived a nonlocal nonlinear partial differential equation which models dynamics roots differentiation. In this paper, we connect rigorously solutions Steinerberger’s PDE evolution for class trigonometric polynomials. Namely...

The traditional conservation of mass equation is derived using a first-order Taylor series to represent flux change in a control volume, which is valid strictly for cases of linear changes in flux through the control volume. We show that using higher-order Taylor series approximations for the mass flux results in mass conservation equations that are intractable. We then show that a fractional T...

where (ai, bj) ∈ R, ν is the commensurable differentiation order,mB and mA are respectively numerator and denominator degrees, with mA > mB for strictly causal systems. Stability of fractional differentiation systems is addressed in the following theorem. Theorem 1.1. (Stability Matignon (1998)). A commensurable transfer function with a commensurable order ν, as in (4), with T and R two coprime...

The problem of normal and anomalous space diffusion is formulated on the basis of the integral equations with various type of the probability transition functions for diffusion (PTD functions). For the cases of stationary and time-independent PTD functions the method of fractional differentiation is avoided to construct the correct probability distributions for arbitrary distances, what is impo...

CRONE control, robust control methodology based on fractional differentiation, is applied to state observer design. State observation can indeed be viewed as a regulation problem given that the goal of a state observer is to cancel the observation errors in spite of measurement noises, disturbances and plant perturbations. This conclusion has been used recently to define a new class of state ob...

This paper deals with the tuning of fractional PID controllers, in which the orders of the integral and derivative parts, λ and μ, respectively, are fractional. The purpose is to take advantage of the introduction of these two parameters and fulfil additional specifications of design. A new method for tuning the fractional PID controller is proposed in this paper. The basic ideas of this new tu...

A fractional diffusion equation based on Riemann-Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of H-functions. It differs from the known solution of fractional diffusion equations based on fractional integrals. The solution of fractional diffusion based on a Riemann-Liouville fractional time derivative...

We show that the response, frozen and semifreddo fractional susceptibility functions of certain real-analytic unimodal families, at Misiurewicz parameters for differentiation index $0\le\eta<1/2$, are holomorphic on a disk radius greater than one. This is step towards solving conjecture Baladi Smania, in case aforementioned functions.

In this paper, we consider an inverse boundary value problem for a mixed type partial differential equation with Hilfer operator of fractional integro-differentiation in positive rectangular domain and spectral parameter negative domain. The depends from another derivatives. With respect to first variable is fractional-order nonhomogeneous the part considering segment, second second-order segme...