共查询到20条相似文献,搜索用时 61 毫秒
1.
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
2.
Based on fractional isospectral problems and general bilinear forms, the generalized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
3.
引入分数阶多分辨分析与分数阶尺度函数的概念.运用时频分析方法与分数阶小波变换,研究了分数阶正交小波的构造方法,得到分数阶正交小波存在的充要条件.给出分数阶尺度函数与小波的分解与重构算法,算法比经典的尺度函数与小波的分解与重构算法更具有一般性. 相似文献
4.
A. Ashyralyev 《Journal of Mathematical Analysis and Applications》2009,357(1):232-236
Definitions of fractional derivatives and fractional powers of positive operators are considered. The connection of fractional derivatives with fractional powers of positive operators is presented. The formula for fractional difference derivative is obtained. 相似文献
5.
Dongling Wang Aiguo Xiao 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):602-610
In this paper, the fractional variational integrators for a class of fractional variational problems are developed. The fractional discrete Euler-Lagrange equation is obtained. Based on the Grünwald-Letnikov method and Diethelm’s fractional backward differences, some fractional variational integrators are presented and the fractional variational errors are discussed. Some numerical examples are presented to illustrate these results. 相似文献
6.
7.
The stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise is considered. Firstly, the generalized harmonic function technique is applied to the fractional self-excited systems. Based on this approach, the original fractional self-excited systems are reduced to equivalent stochastic systems without fractional derivative. Then, the analytical solutions of the equivalent stochastic systems are obtained by using the stochastic averaging method. Finally, in order to verify the theoretical results, the two most typical self-excited systems with fractional derivative, namely the fractional van der Pol oscillator and fractional Rayleigh oscillator, are discussed in detail. Comparing the analytical and numerical results, a very satisfactory agreement can be found. Meanwhile, the effects of the fractional order, the fractional coefficient, and the intensity of Gaussian white noise on the self-excited fractional systems are also discussed in detail. 相似文献
8.
Guy Jumarie 《Applied Mathematics Letters》2010,23(12):1444-1450
The modified Riemann–Liouville fractional derivative applies to functions which are fractional differentiable but not differentiable, in such a manner that they cannot be analyzed by means of the Djrbashian fractional derivative. It provides a fractional Taylor’s series for functions which are infinitely fractional differentiable, and this result suggests introducing a definition of analytic functions of fractional order. Cauchy’s conditions for fractional differentiability in the complex plane and Cauchy’s integral formula are derived for these kinds of functions. 相似文献
9.
Hui Wang Tie-Cheng Xia 《Communications in Nonlinear Science & Numerical Simulation》2013,18(10):2859-2867
In this paper, a fractional supertrace identity on superalgebras and Hamiltonian structure of the fractional soliton equation hierarchy are presented by using the modified Riemann–Liouville derivative and exterior derivatives of fractional orders. As applications, we get the fractional super Jaulent–Miodek (JM) hierarchy and its super Hamiltonian structure by using fractional supertrace identity. This method can be used to get more fractional super hierarchies. 相似文献
10.
11.
In this present article, we study the fractional Hankel transform and its inverse on certain Gel'fand‐Shilov spaces of type S. The continuous fractional wavelet transform is defined involving the fractional Hankel transform. The continuity of fractional Hankel wavelet transform is discussed on Gel'fand‐Shilov spaces of type S. This article goes further to discuss the continuity property of fractional Hankel transform and fractional Hankel wavelet transform on the ultradifferentiable function spaces. 相似文献
12.
In this paper fractional Hindmarsh Rose (HR) neuron, which mimics several behaviors of a real biological neuron is implemented on field programmable gate array (FPGA). The results show several differences in the dynamic characteristics of integer and fractional order Hindmarsh Rose neuron models. The integer order model shows only one type of firing characteristics when the parameters of model remains same. The fractional order model depicts several dynamical behaviors even for the same parameters as the order of the fractional operator is varied. The firing frequency increases when the order of the fractional operator decreases. The fractional order is therefore key in determining the firing characteristics of biological neurons. To implement this neuron model first the digital realization of different fractional operator approximations are obtained, then the fractional integrator is used to obtain the low power and low cost hardware realization of fractional HR neuron. The fractional neuron model has been implemented on a low voltage and low power circuit and then compared with its integer counter part. The hardware is used to demonstrate the different dynamical behaviors of fractional HR neuron for different type of approximations obtained for fractional operator in this paper. A coupled network of fractional order HR neurons is also implemented. The results also show that synchronization between neurons increases as long as coupling factor keeps on increasing. 相似文献
13.
本文首先运用迭代法获得一类含多项Riemann-Liouville型分数阶导数的微分方程的连续通解,然后应用数学归纳法得到这类脉冲微分方程的分片连续通解. 所得结果归结于脉冲分数阶微分方程领域,对分数阶微分方程研究者有参考意义. 相似文献
14.
Ashwini D. Mali Kishor D. Kucche 《Mathematical Methods in the Applied Sciences》2020,43(15):8608-8631
In this paper, we derive the equivalent fractional integral equation to the nonlinear implicit fractional differential equations involving Ψ-Hilfer fractional derivative subject to nonlocal fractional integral boundary conditions. The existence of a solution, Ulam–Hyers, and Ulam–Hyers–Rassias stability have been acquired by means of an equivalent fractional integral equation. Our investigations depend on the fixed-point theorem due to Krasnoselskii and the Gronwall inequality involving Ψ-Riemann–Liouville fractional integral. Finally, examples are provided to show the utilization of primary outcomes. 相似文献
15.
Won Sang Chung Soroush Zare Hassan Hassanabadi Elham Maghsoodi 《Mathematical Methods in the Applied Sciences》2020,43(11):6950-6967
In this paper, the deformation of the ordinary quantum mechanics is formulated based on the idea of conformable fractional calculus. Some properties of fractional calculus and fractional elementary functions are investigated. The fractional wave equation in 1 + 1 dimension and fractional version of the Lorentz transformation are discussed. Finally, the fractional quantum mechanics is formulated; infinite potential well problem, density of states for the ideal gas, and quantum harmonic oscillator problem are discussed. 相似文献
16.
A.S. Hegazi E. Ahmed A.E. Matouk 《Communications in Nonlinear Science & Numerical Simulation》2013,18(5):1193-1202
In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigated. We also obtain the necessary condition for the existence of chaotic attractors in the commensurate fractional order Liu system. The effect of fractional order on chaos control of this system is revealed by showing that the commensurate fractional order Liu system is controllable just in the fractional order case when using a specific choice of controllers. Moreover, we achieve chaos synchronization between the commensurate fractional order Liu system and its integer order counterpart via function projective synchronization. Numerical simulations are used to verify the analytical results. 相似文献
17.
The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations 下载免费PDF全文
Santanu Saha Ray 《Mathematical Methods in the Applied Sciences》2017,40(5):1637-1648
In this paper, numerical solutions of fractional Fokker–Planck equations with Riesz space fractional derivatives have been developed. Here, the fractional Fokker–Planck equations have been considered in a finite domain. In order to deal with the Riesz fractional derivative operator, shifted Grünwald approximation and fractional centred difference approaches have been used. The explicit finite difference method and Crank–Nicolson implicit method have been applied to obtain the numerical solutions of fractional diffusion equation and fractional Fokker–Planck equations, respectively. Numerical results are presented to demonstrate the accuracy and effectiveness of the proposed numerical solution techniques. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
孟伟 《数学的实践与认识》2020,(8):192-198
给出了分数阶灰色累减生成算子的详细推导过程,并证明了分数阶灰色累减生成算子的不动点定理、信息优先原理、交换律与指数律,为分数阶灰色预测模型提供了理论基础.算例验证了分数阶灰色累减生成算子的特征,在灰色预测模型GM(1,1)中的应用证明了分数阶灰色累减生成算子的有效性. 相似文献
19.
Guotao Wang Xueyan Ren Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2020,43(5):2646-2655
The purpose of the current study is to investigate IBVP for spatial-time fractional differential equation with Hadamard fractional derivative and fractional Laplace operator(−Δ)β. A new Hadamard fractional extremum principle is established. Based on the new result, a Hadamard fractional maximum principle is also proposed. Furthermore, the maximum principle is applied to linear and nonlinear Hadamard fractional equations to obtain the uniqueness and continuous dependence of the solution of the IBVP at hand. 相似文献
20.
Sergiu I. Vacaru 《Chaos, solitons, and fractals》2012,45(9-10):1266-1276
We formulate the fractional Ricci flow theory for (pseudo) Riemannian geometries enabled with nonholonomic distributions defining fractional integro-differential structures, for non-integer dimensions. There are constructed fractional analogs of Perelman’s functionals and derived the corresponding fractional evolution (Hamilton’s) equations. We apply in fractional calculus the nonlinear connection formalism originally elaborated in Finsler geometry and generalizations and recently applied to classical and quantum gravity theories. There are also analyzed the fractional operators for the entropy and fundamental thermodynamic values. 相似文献