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Our goal is to prove the existence of a connection between fractal geometries and fractional calculus. We show that such a connection exists and has to be sought in the physical origins of the power laws ruling the evolution of most of the natural phenomena, and that are the characteristic feature of fractional differential operators. We show, with the aid of a relevant example, that a power law comes...
The aim of the paper is to consider - in base on classical models and numerical simulations - fractional model of the type of Hegselmann and Krause (FHK) taking into account memory of states. One of our hypothesis is that fractional operators will include memory of the system to the whole process. Then we are going to examine and to do an analyze with verification of properties of this fractional...
Provides an abstract for each of the keynote presentations and a brief professional biography of each presenter. The complete presentations were not made available for publication as part of the conference proceedings.
In this paper the viscoelastic behavior of pultruded beams has been examined. Pultruded beams are constituted by a polymer infilled with reinforcement in longitudinal direction, while in the orthogonal direction no fiber are present for technological reasons. As a consequence the material has two different behaviors in longitudinal and in orthogonal directions. It follows that pultruded beams are...
Different types of boundary conditions for the time-fractional heat conduction equation in a bounded domain are examined. A composed solid consisting of three domains is considered. Assuming that the thickness of the intermediate domain is small with respect to two other sizes and is constant, a three-dimensional heat conduction problem in the intermediate domain is reduced to the two-dimensional...
The problem of cosmic rays reacceleration (secondary acceleration) in the interstellar galactic medium is considered with the use of fractional differential equations. Involving the fractional operator is justified by by taking into account non-uniform (fractal-type) time-distribution of the acceleration events possible connected with diffusion type of spatial motion.
The Riemann-Liouville-type fractional order difference initial value problems for linear systems are discussed. The classical Z-transform method is used to give the possible solutions of the considered systems. The formulas for the Z-transform of some functions, fractional summation and difference operators are presented.
The Riemann-Liouville and Caputo derivatives are analysed in the context of the linear system theory. For it an analysis framework is presented. It is shown that those derivatives are unsuitable for studying the linear systems and in particular define transfer function.
In this article, we derive the Sheffer polynomials {Sm(x, y)}m=1∞ in two variables as the coefficient set of the generating function A(t, y)ext, where A(s, y) is a complex function with respect to complex variable s and y ϵ R. When the function A(s, y) is entire, using the inverse Mellin transform we get the coefficient set, and when the function A(s, y) has a branch point at zero point s = 0, using...
A new frequency-domain algorithm for optimization of PID regulators having a fractional differential compensator connected in series (PIDCα) has been developed. The adjustable parameters of the regulator are: proportional gain k, integral gain ki, relative attenuation factor of PID zeros ζ, zero of the fractional differential compensator -1/τ and fractional power a of the differential compensator...
In quantum mechanics, the Heisenberg's uncertainty principle is an inequalities which it says that we can not measure the conjugate quantities of the particles at the same time with the precision. The fuzzy boundary condition can be a mathematical model for this type of problem. In this paper we consider the Schrödinger equation equipped with fuzzy conditions. The analytical result is derived and...
In a recent article we have introduced and used the complex fractional wavelet for QRS complex detection in ECG signal. This complex fractional wavelet is derived from the Cole-Cole distribution which is widely used in the modeling of dielectrics by a fractional power pole. This work presents an extension of QRS detection scheme using the complex Morlet wavelet function. It consists of using the real...
Considering that the vehicle state error derives from the different initial states and parameters between the real vehicle model and the reference model, fractional sliding model control is proposed for the active four-wheel steering vehicle. Optimal control is adopted to design the sliding mode in order to eliminate the state error caused by the different initial states. On this basis, fractional...
Dynamical properties of viscoelastic material are considered to be originated from the complex combination of elastic components and viscous components. From this idea, the time derivative of deviatoric part of the stress of elastic components have been integrated by fractional order. In this paper, several fractional derivative models for large extension are proposed based on this idea. The fractional...
This paper presents some results for stability analysis of fractional order polynomials using the Hermite-Biehler theorem. The possibilities of the extension of the Hermite-Biehler theorem to fractional order polynomials is investigated and it is observed that the Hermite-Biehler theorem can be an effective tool for the stability analysis of fractional order polynomials. Variable changing has been...
A novel formulation for Fractional Tuned Mass Damper (FTMD) devices is proposed in this paper. The FTMD is realized by connecting an oscillating mass to the main structure using a viscoelastic link, realized through elastomeric rubber bearings with fractional derivative constitutive model. A new function, labeled Damped Fractional Frequency, is defined for the fractional oscillator as the analogous...
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