Application of Scans and Fractional Power Integrands

2004 ◽  
pp. 19-31 ◽  
Author(s):  
Thierry De Pauw ◽  
Robert Hardt
Keyword(s):  
Fractional Power

scholarly journals Reduced basis approximations of the solutions to spectral fractional diffusion problems

2020 ◽  
Vol 28 (3) ◽  
pp. 147-160
Author(s):  
Andrea Bonito ◽  
Diane Guignard ◽  
Ashley R. Zhang
Keyword(s):  
Computational Cost ◽  
Fractional Power ◽  
Reaction Diffusion ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Quadrature Point ◽  
Reduced Basis ◽  
Fast Evaluation ◽  
Bottle Neck ◽  
Diffusion Problems

AbstractWe consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral approximated via quadratures. At each quadrature point, a reaction–diffusion problem must be approximated and is the method bottle neck. In this work, we propose to reduce the computational cost using a reduced basis strategy allowing for a fast evaluation of the reaction–diffusion problems. The reduced basis does not depend on the fractional power s for 0 < smin ⩽ s ⩽ smax < 1. It is built offline once for all and used online irrespectively of the fractional power. We analyze the reduced basis strategy and show its exponential convergence. The analytical results are illustrated with insightful numerical experiments.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

Continuous Finite-Time Torque Control for Flexible Assistance Exoskeleton with Delay Variation Input

Robotica ◽  
2020 ◽  
pp. 1-26
Author(s):  
Tao Xue ◽  
ZiWei Wang ◽  
Tao Zhang ◽  
Ou Bai ◽  
Meng Zhang ◽  
...  
Keyword(s):  
Finite Time ◽  
Disturbance Rejection ◽  
High Performance ◽  
Control Strategies ◽  
Fractional Power ◽  
Critical Issue ◽  
Human Robot Interaction ◽  
Torque Control ◽  
Finite Time Stability ◽  
Control Scheme

SUMMARY Accurate torque control is a critical issue in the compliant human–robot interaction scenario, which is, however, challenging due to the ever-changing human intentions, input delay, and various disturbances. Even worse, the performances of existing control strategies are limited on account of the compromise between precision and stability. To this end, this paper presents a novel high-performance torque control scheme without compromise. In this scheme, a new nonlinear disturbance observer incorporated with equivalent control concept is proposed, where the faster convergence and stronger anti-noise capability can be obtained simultaneously. Meanwhile, a continuous fractional power control law is designed with an iteration method to address the matched/unmatched disturbance rejection and global finite-time convergence. Moreover, the finite-time stability proof and prescribed control performance are guaranteed using constructed Lyapunov function with adding power integrator technique. Both the simulation and experiments demonstrate enhanced control accuracy, faster convergence rate, perfect disturbance rejection capability, and stronger robustness of the proposed control scheme. Furthermore, the evaluated assistance effects present improved gait patterns and reduced muscle efforts during walking and upstair activity.

scholarly journals Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

2017 ◽  
Vol 4 (1) ◽  
pp. 1-15
Author(s):  
Machindra B. Dhakne ◽  
Poonam S. Bora
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Fractional Power ◽  
Strong Solutions ◽  
Fractional Power Of Operators

Abstract In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

Studies of Chromium Removal from Tannery Effluents by Dead Streptomyces Rimosus

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
Mohamed Nasser Sahmoune ◽  
Krim Louhab ◽  
Aissa Boukhiar
Keyword(s):  
Fractional Power ◽  
Kinetic Studies ◽  
Second Order ◽  
Order Kinetic ◽  
Streptomyces Rimosus ◽  
Tannery Effluents ◽  
Equilibrium Data ◽  
Order Kinetic Model ◽  
Pseudo Second Order ◽  
Ph Range

Dead streptomyces rimosus was found to be an effective biosorbent for the removal of chromium from industrial tanning effluents. A sorption level of 65 mg/g was observed at pH 4.8 while the precipitation effect augmented this value at a higher pH range. Chromium desorption increased with decreasing desorption agents pH (including HCl and H2SO4) to a maximum value of 95% at approximately zero pH. The biosorption data of trivalent chromium by streptomyces rimosus has been used for kinetic studies based on fractional power, Elovich, pseudo-first order and pseudo-second order rate expressions. The time-dependent Cr (III) biosorption data were well-described by a pseudo-second-order kinetic model. The intraparticle diffusion is not the rate-limiting step for the whole reaction. It was found that the biosorption equilibrium data fit well with the Langmuir model.

Some remarks on the solvability of non-local elliptic problems with the Hardy potential

2014 ◽  
Vol 16 (04) ◽  
pp. 1350046 ◽  
Author(s):  
B. Barrios ◽  
M. Medina ◽  
I. Peral
Keyword(s):  
Real Number ◽  
Sobolev Inequality ◽  
Positive Real Number ◽  
Fractional Power ◽  
Existence Of Solution ◽  
Sharp Constant ◽  
Hardy Potential ◽  
Positive Real ◽  
Existence And Multiplicity ◽  
Non Local

The aim of this paper is to study the solvability of the following problem, [Formula: see text] where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded domain such that 0 ∈ Ω, μ is a positive real number, λ < ΛN,s, the sharp constant of the Hardy–Sobolev inequality, 0 < q < 1 and [Formula: see text], with αλ a parameter depending on λ and satisfying [Formula: see text]. We will discuss the existence and multiplicity of solutions depending on the value of p, proving in particular that p(λ, s) is the threshold for the existence of solution to problem (Pμ).

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