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Tatiana Odzijewicz Agnieszka B. Malinowska Delfim F. M. Torres 《Central European Journal of Physics》2013,11(6):691-701
We prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo. 相似文献
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A. N. Bogolyubov A. A. Koblikov D. D. Smirnova N. E. Shapkina 《Moscow University Physics Bulletin》2012,67(5):423-428
Electromagnetic fields in time-dispersion media with a power-law dependence on time are analyzed. It is shown that these media are fractal and their fractal dimension is determined. Equations for scalar and vector potentials are derived using analogues of Maxwell??s equations for these types of media with the use of Caputo fractional derivatives. Electromagnetic fields in a bounded domain are numerically calculated for arbitrary functions of charge and current. 相似文献
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分数阶系统具有更大的密钥空间, 然而异结构的分数阶系统在保密通信领域更具有普遍性, 因此, 研究异结构的分数阶同步问题具有重要的意义. 本文讨论了分数阶超混沌Chen系统和分数阶超混沌Rössler系统的异结构同步问题, 基于分数阶系统稳定性理论, 应用主动控制同步法和自适应控制同步法来设计各自不同的控制器, 使得响应系统和驱动系统同步. 数值仿真表明了本文所研究方法的可行性和有效性. 相似文献
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In this paper, we discuss nonlocal Cauchy problems for fractional order nonlinear differential systems. Firstly, an important matrix associated with fractional order and two functionals are constructed. Further, some sufficient conditions which guarantee such matrix convergent to zero matrix are presented. Secondly, by using three fixed point theorems via the techniques that use convergent to zero matrix and vector norm, some existence results for the solutions of such fractional order nonlinear differential systems are given under different conditions. Finally, some examples are given to illustrate the results. 相似文献
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A fractional order model for nonlocal epidemics is given. Stability of fractional order equations is studied. The results are expected to be relevant to foot-and-mouth disease, SARS and avian flu. 相似文献
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Sachin Bhalekar 《Central European Journal of Physics》2013,11(10):1514-1522
Fractional order version of a dynamical system introduced by Yu and Wang (Engineering, Technology & Applied Science Research, 2, (2012) 209–215) is discussed in this article. The basic dynamical properties of the system are studied. Minimum effective dimension 0.942329 for the existence of chaos in the proposed system is obtained using the analytical result. For chaos detection, we have calculated maximum Lyapunov exponents for various values of fractional order. Feedback control method is then used to control chaos in the system. Further, the system is synchronized with itself and with fractional order financial system using active control technique. Modified Adams-Bashforth-Moulton algorithm is used for numerical simulations. 相似文献
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时延估计技术是一项活跃的研究课题。近年来,满足稳定分布的脉冲噪声模型得到了广泛的研究,并在时延估计技术中得到了应用。为提高时延估计方法在脉冲噪声环境下的估计精度和稳定性,本文提出了一种改进的基于分数低阶协方差谱的广义互相关时延估计方法,并进一步引入经验参数对所提出方法的性能进行调整。仿真分析表明,新方法在高斯和脉冲噪声环境条件下都具有良好的顽健性。 相似文献
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The current method for modelling magnetic core coils involves the use of an ohmic resistance connected in parallel to the ideal inductance to describe the related hysteresis and eddy-current losses. 相似文献
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The names of Grünwald and Letnikov are associated with discrete convolutions of mesh h, multiplied by h−α. When h tends to zero, the result tends to a Marchaud’s derivative (of the order of α) of the function to which the convolution is applied. The weights of such discrete convolutions form well-defined sequences, proportional to k−α−1 near infinity, and all moments of integer order r<α are equal to zero, provided α is not an integer. We present a continuous variant of Grünwald-Letnikov formulas, with integrals instead of series. It involves a convolution kernel which mimics the above-mentioned features of Grünwald-Letnikov weights. A first application consists in computing the flux of particles spreading according to random walks with heavy-tailed jump distributions, possibly involving boundary conditions. 相似文献
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Hossein Jafari Khosro Sayevand Haleh Tajadodi Dumitru Baleanu 《Central European Journal of Physics》2013,11(10):1523-1527
In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented. 相似文献
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We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M=+∞, M=4k(k is a natural number), and M=4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided. 相似文献
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V. R. Figerou 《Communications in Mathematical Physics》1981,79(3):401-433
Using functional approaches, we investigate the large-K behaviour of theK th coefficientE k in the perturbation expansion for the ground-state energyE(g) of the generalized anharmonic oscillatorX 2N with internalO(n)-symmetry. We establish the equivalence between the pure functional approach and the method of Collins-Soper at any order in 1 /K. For that purpose, we first develop an algebraic treatment of perturbation series and prove a theorem on Borelsummable functions. Finally, we compute analytically the 1 /K and 1 /K 2 corrections to the leading term forN=2. 相似文献
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Mohammad Saleh Tavazoei 《Physica D: Nonlinear Phenomena》2008,237(20):2628-2637
In this paper, based on the stability theorems in fractional differential equations, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system. This condition is proposed for incommensurate order systems in general, but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems. Though the presented condition is only a necessary (and not sufficient) condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system, chaotic attractors can not be observed and for what parameters and orders, the system may generate chaos. It can also be used as a tool to confirm or reject results of a numerical simulation. Some of the numerical results reported in the previous literature are confirmed by this tool. 相似文献
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Control of fractional chaotic and hyperchaotic systems based on a fractional order controller
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We present a new fractional-order controller based on the Lyapunov stability theory and propose a control method which can control fractional chaotic and hyperchaotic systems whether systems are commensurate or incommensurate.The proposed control method is universal, simple, and theoretically rigorous. Numerical simulations are given for several fractional chaotic and hyperchaotic systems to verify the effectiveness and the universality of the proposed control method. 相似文献
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For the Grimus-Stockinger formula the same dimensionless parameter of asymptotic expansion is found by several ways of calculations. This parameter strongly depends on the width of wave packet. 相似文献
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Modified impulsive synchronization of fractional order hyperchaotic systems 总被引:1,自引:0,他引:1
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In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method. 相似文献