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INFINITELY MANY SOLUTIONS WITH PEAKS FOR A fractional system IN R^N

Acta Mathematica Scientia 2020年第2期40卷 389-411页

作者： Qihan HE Yanfang PENG Department of Mathematics and Information Science Guangxi Center for Mathematical ResearchGuangxi UniversityNanning 530003China School of Mathematics Science Guizhou Normal UniversityGuiyang 550001China

In this article,we consider the following coupled fractional nonlinear Schrödinger system in R^{(−Δ)su+P(x)u=μ1|u|^2p−2u+β|u|p|u|p−2u,x∈RN,(−Δ)sv+Q(x)v=μ2|v|^2p−2v+β|v|p|v|p−2v,x∈RN,u,v∈Hs(RN),where N≥2,00,μ2>0 andβ∈R is a coupling *** prove that it has infinitely many non-radial positive solutions under some additional conditions on P(x),Q(x),p andβ.More precisely,we will show that for the attractive case,it has infinitely many non-radial positive synchronized vector solutions,and for the repulsive case,infinitely many non-radial positive segregated vector solutions can be found,where we assume that P(x)and Q(x)satisfy some algebraic decay at infinity.

关键词： fractional system solutions with peaks synchronized segregated

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Stabilization of fractional bilinear systems with multiple inputs

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Applied Mathematics(A Journal of Chinese Universities) 2023年第1期38卷 78-88页

作者： Thouraya Kharrat Fehmi Mabrouk Fawzi Omri Department of Mathematics Faculty of Sciences of SfaxUniversity of SfaxTunisia

In this paper,we study in a constructive way the stabilization problem of fractional bilinear systems with multiple *** the quadratic Lyapunov functions and some additional hypotheses on the unit sphere,we construct stabilizing feedback laws for the considered fractional bilinear system.A numerical example is given to illustrate the efficiency of the obtained result.

关键词： stabilization fractional system bilinear system multiple inputs Lyapunov functions

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Resonance and Bifurcation of fractional Nonlinear systems with Power Damping Term for Robot Grinding

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Journal of Beijing Institute of Technology 2023年第1期32卷 23-40页

作者： Wei Shi Qingxue Huang Jinzhu Zhang Tao Wang Ziliang Li Yanjie Zhang Xiaoyan Xiong College of Mechanical and Vehicle Engineering Taiyuan University of TechnologyTaiyuan 030024China Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment Ministry of EducationTaiyuan University of TechnologyTaiyuan 030024China Institute of Advanced Forming and Intelligent Equipment Taiyuan University of TechnologyTaiyuan 030024China

A fractional nonlinear system with power damping term is introduced to study the forced vibration system in order to solve the resonance and bifurcation problems between grinding wheel and steel bar during robot *** robot,grinding wheel and steel bar are reduced to a spring-damping second-order system *** implicit function equations of vibration amplitude of the dynamic system with coulomb friction damping,linear damping,square damping and cubic damping are obtained by average *** stability of the system is analyzed and explained,and the stability condition of the system is ***,the amplitude-frequency characteristic curves of the system under different fractional differential orders,nonlinear stiffness parameters,fractional differential term coefficients and external excitation amplitude are *** is shown that the fractional differential term in the dynamic system is the damping *** the influence of four kinds of damping on the vibration amplitude of the system under the same parameter is investigated and it is proved that the cubic damping suppresses the vibration of the system to the maximum ***,based on the idea that the equilibrium point of the system is the constant part of the Fourier series expansion term,the bifurcation behavior caused by the change of damping parameters in linear damping,square damping and cubic damping systems with different values of fractional differential order is investigated.

关键词： robot grinding fractional system average method power damping resonance and bifurcation

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fractional Adaptive Kalman Filter with Colored Correlated Noise

Fractional Adaptive Kalman Filter with Colored Correlated No...

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第40届中国控制会议

作者： Xinhe Wang Xiaojun Sun Electrical Engineering Institute Heilongjiang University

For linear fractional systems with correlated fractional colored process noise and colored measurement noise obtained by Tustin generating function method, a fractional adaptive Kalman filter based on virtual noise technology is proposed in this paper, which can effectively realize the state estimation of such fractional systems. The proposed algorithm is simple and more suitable for practical engineering applications. Simulation results verify the effectiveness and feasibility of the proposed algorithm.

关键词： fractional system fractional Kalman filtering adaptive filtering colored noises correlated noises

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