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Identification of System with Distributed-Order Derivatives

Fractional Calculus and Applied Analysis, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Duan, Jun-Sheng, Li, Yu
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Optimal Space Distributed Order-Preserving Lists

Journal of Algorithms, 1999
Summary: A move-to-front list is a distributed data object that provides an abstraction of a temporal ordering on a set of processes in a distributed system. We present a lower bound and a matching upper bound of \(\Theta(\log^2 n)\) bits on the space per processor needed to implement such a list using single-writer multiple-reader registers.
Saks, Michael, Zaharoglou, Fotios
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Distributed-Order Filtering and Distributed-Order Optimal Damping

2012
The idea of using the distributed-order differential equation first proposed by Caputo in (1969) is at least mathematically interesting as demonstrated in the previous chapters. However, people may question its usefulness in engineering practice. In this chapter, we included two generic applications.
Zhuang Jiao   +2 more
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On distributed order integrator/differentiator

Signal Processing, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Yan, Sheng, Hu, Chen, Yang Quan
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Variable Order and Distributed Order Fractional Operators

Nonlinear Dynamics, 2002
Many physical processes appear to exhibit fractional order behaviour that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. The paper develops the concept of variable and distributed order fractional operators.
Lorenzo, Carl F., Hartley, Tom T.
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On a fractional distributed-order oscillator

Journal of Physics A: Mathematical and General, 2005
Summary: We consider a viscoelastic rod with a concentrated mass at its end. The mass is moving along the straight line that coincides with the rod axis. The mass is connected by a linear spring, and a known active force is acting on it. We assume that the rod is light and is described by fractional dissipation.
Atanacković, Teodor   +2 more
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On the distributed order PID controller

AEU - International Journal of Electronics and Communications, 2017
Abstract This paper proposes a generalized fractional controller that covers the complete range of differintegrators of order −1 to order 1. This controller is named distributed order PID controller (DOPID) due to the fact that it broadens the structure of the conventional PID controller.
Boris B. Jakovljević   +3 more
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Distributed order model of labor migration

International Journal of Nonlinear Sciences and Numerical Simulation, 2022
Abstract In this study, we present a mathematical model of socio-economic process of labor force migration. We present our model in the terms of distributed order fractional partial differential equation. The proposed model involves time varying diffusion coefficient.
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On distributed order low-pass filter

Proceedings of 2010 IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications, 2010
In this paper, we derive the impulse response of the fractional distributed order low-pass filters. Based on the derived analytical impulse response, a method on how to perform the discretization of the above distributed order low-pass filters is presented. Time and frequency domains illustrations are provided.
Yan Li, Hu Sheng, YangQuan Chen
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Distributed-order relaxation-oscillation equation

AIP Conference Proceedings
In this short paper, we study the Cauchy problem associated with the forced time-fractional relaxation-oscillation equation with distributed order. We employ the Laplace transform technique to derive the solution. Additionally, for the scenario without external forcing, we focus on density functions characterized by a single order, demonstrating that ...
Rodrigues, M. M.   +2 more
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