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1.
In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation. 相似文献
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The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained
in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with fractional integral
equations. The results derived in this paper provide an extension of a result given by Haubold and Mathai in a recent paper
(Haubold and Mathai, 2000).
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
I. Ben-Israel T. Piran Aharon Eviatar J. Weinstock 《Astrophysics and Space Science》1975,38(1):125-155
A statistical theory, previously developed for electrostatic waves is extended to the case of electromagnetic waves in the presence of a constant magnetic field. The theory is nonlinear and contains the effects of mode-mode coupling. The extension is not straightforward as assumed previously by many authors and involves calculation of perturbed trajectories in both velocity and configuration space. A diffusion equation is derived for the average particle distribution function, the associated diffusion tensor is calculated and a nonlinear wave dispersion relation is found. All these results contain the usual quasilinear theory as the lowest order approximation. 相似文献
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A Certain Class of Laplace Transforms with Applications to Reaction and Reaction-Diffusion Equations
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, α-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations. 相似文献
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A. Nazari-Golshan S. S. Nourazar P. Parvin H. Ghafoori-Fard 《Astrophysics and Space Science》2014,349(1):205-214
The time fractional modified KdV, the so-called TFMKdV equation is solved to study the nonlinear propagation of the dust acoustic (DA) solitary waves in un-magnetized four components dusty plasma. This plasma consists of positively charged warm adiabatic dust, negatively charged cold dust, non-isothermal electrons and Maxwellian ions. The TFMKdV equation is derived by using semi-inverse and Agrawal’s method and solved by the Laplace Adomian decomposition method (LADM). The effects of the time fractional order (β), the ratio of dust to ion temperature (δ d ), the time (τ), the mass and charge ratio (α), the non-isothermal parameter (γ) and wave velocity (v) on the DA solitary wave are studied. Our results show that the variations of the amplitude of DA solitary wave versus (γ) are in agreement with the results obtained previously. Moreover, the time fractional order plays a role of higher order perturbation in modulating the soliton shape. The achievements of this research for the DA solitary waves may be applicable in space plasma environments and laboratory plasmas. 相似文献
8.
The nonlinear propagation of ion acoustic waves in an ideal plasmas containing degenerate electrons is investigated. The Korteweg-de-Vries
(K-dV) equation is derived for ion acoustic waves by using reductive perturbation method. The analytical traveling wave solutions
of the K-dV equation investigated, through the (G′/G)-expansion method. These traveling wave solutions are expressed by hyperbolic function, trigonometric functions are rational
functions. When the parameters are taken special values, the solitary waves are derived from the traveling waves. Also, numerically
the effect different parameters on these solitary waves investigated and it is seen that exist only the compressive solitary
waves in Thomas-Fermi plasmas. 相似文献
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The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring. 相似文献
10.
The oscillatory modes of a magnetically twisted compressible flux tube embedded in a compressible magnetic environment are investigated in cylindrical geometry. Solutions to the governing equations to linear wave perturbations are derived in terms of Whittaker’s functions. A general dispersion equation is obtained in terms of Kummer’s functions for the approximation of weak and uniform internal twist, which is a good initial working model for flux tubes in solar applications. The sausage, kink and fluting modes are examined by means of the derived exact dispersion equation. The solutions of this general dispersion equation are found numerically under plasma conditions representative of the solar photosphere and corona. Solutions for the phase speed of the allowed eigenmodes are obtained for a range of wavenumbers and varying magnetic twist. Our results generalise previous classical and widely applied studies of MHD waves and oscillations in magnetic loops without a magnetic twist. Potential applications to solar magneto-seismology are discussed. 相似文献
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In view of the usefulness and a great importance of the kinetic equation in certain astrophysical problems the authors develop a new and further generalized form of the fractional kinetic equation involving the G-function, a generalized function for the fractional calculus. This new generalization can be used for the computation of the change of chemical composition in stars like the Sun. The Mellin-Barnes contour integral representation of the G-function is also established. The manifold generality of the G-function is discussed in terms of the solution of the above fractional kinetic equation. A compact and easily computable solution is established. Special cases, involving the generalized Mittag-leffler function and the R-function, are considered. The obtained results imply more precisely the known results. 相似文献
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Rabindra Nath Das 《Astrophysics and Space Science》2008,317(1-2):119-126
The linear singular integral equation derived from the nonlinear integral equation of Chandrasekhar’s H-function in radiative transfer is considered here to develop a new form of H-function as a solution of a Riemann–Hilbert problem using Plemelj and Cauchy integral formulae for complex domain. This new form of H-function is a simple integral of known functions. Forms of H-function both for conservative and nonconservative cases are obtained. Their numerical evaluations are made by Simpson’s one-third rule to arrive at an accuracy to ninth places of decimals. 相似文献
13.
A single layer fractional orthogonal neural network for solving various types of Lane–Emden equation
《New Astronomy》2020
Lane–Emden equation is an important nonlinear singular second order differential equation which can express various phenomena in astrophysics. On the other hand, by growing accessible data and information of physical dynamics, solving differential equations by data-driven algorithms becomes more significant. In this paper, an artificial neural network framework is provided to approximate the solution of different types of Lane–Emden equation such as fractional order or system of Lane–Emden equation. The presented neural network is a single layer orthogonal network. We use fractional order of Legendre functions as active functions of the hidden layer. Moreover, the Levenberg–Marquardt algorithm is used to train this neural network. In order to show the efficiency and the accuracy of the presented algorithm, we test it on several examples and compare with some other numerical methods. The obtained numerical results show that this network is extremely accurate and feasible. For example, in fractional version of Lane–Emden equation the obtained accuracy is about while it was about in some other methods. 相似文献
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In this paper we have proposed certain generalizations of anomalous diffusion equations for fractional order. These diffusion equations are solved by the method of Laplace transform with respect to the time variable and Fourier transform with respect to the space variable. The solutions of some known diffusion equations are also shown to be derived here. 相似文献
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Harendra Singh 《Astrophysics and Space Science》2018,363(4):71
The key purpose of this article is to introduce an efficient computational method for the approximate solution of the homogeneous as well as non-homogeneous nonlinear Lane-Emden type equations. Using proposed computational method given nonlinear equation is converted into a set of nonlinear algebraic equations whose solution gives the approximate solution to the Lane-Emden type equation. Various nonlinear cases of Lane-Emden type equations like standard Lane-Emden equation, the isothermal gas spheres equation and white-dwarf equation are discussed. Results are compared with some well-known numerical methods and it is observed that our results are more accurate. 相似文献
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Propagation of ion acoustic waves in plasmas containing electrons, positrons and high relativistic ions is investigated. It
is shown that the Korteweg-de Vries (KdV) equation describes the nonlinear waves in this media. The amplitude and energy of
the KdV solitary waves are derived and the effects of relativistic ions on these quantities are discussed. 相似文献
17.
提出了一种适用于天基空间目标光学观测的初始轨道确定新方法. 通过对比地基和天基观测的几何构型, 分析了利用天基光学观测数据进行初轨确定时计算收敛到观测平台自身轨道的原因. 基于轨道半通径方程和改进Gauss方程, 推导出了斜距条件方程组的解析形式, 将天基光学观测的初轨确定问题转换为求解关于观测时刻斜距变量的非线性条件方程组的问题. 利用轨道能量约束减小了解的搜索区域, 消除了方程组的奇点. 最后利用天基实测数据验证并分析了非线性条件方程组根的性质, 利用低轨光学观测平台对低、中、高轨和大椭圆轨道空间目标的仿真观测数据验证了方法的有效性. 相似文献
18.
The nonlinear propagation of ion-acoustic solitary and shock waves in a dissipative, nonplanar quantum plasma comprised of electrons, positrons, and ions are studied. A modified Korteweg-de Vries Burgers equation is derived in the limit of low frequency and long wavelength by taking into account the kinematic viscosity among the plasma constituents. It is shown that this plasma system supports the propagation of both compressive and rarefactive nonlinear waves. The effects of variation of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision of solitary waves are discussed. It is found that these parameters have significant effects on the properties of nonlinear waves in cylindrical and spherical geometries, and these effects for compressive and rarefactive nonlinear waves are obviously different. 相似文献
19.
Singh P. R. Saad Farid A. I. Singh A. K. Pant T. K. Aly Ayman A. 《Astrophysics and Space Science》2021,366(5):1-6
We are considering the spacetime described by the metric proposed by Mannheim and Kazanas. The effective potential and the circular orbits are discussed. The rotational velocity derived from the geodesics equation agrees with the observed flat galactic rotation curves. Finally, solutions to the Gordon equation for massless bosons evolving in this spacetime are obtained in terms of Heun general functions.
相似文献20.
In this paper, we define a hierarchy of distribution functions for simultaneous velocity, magnetic, and temperature fields. Some properties of the constructed distribution functions such as reduction, separation, and coincidence are discussed. Equations for the evolution of one- and two-point distribution functions have been derived. Finally, a comparison of the equation for the single-point distribution function in case of zero viscosity, negligible diffusivity, and infinite electrical conductivity is made with first equation of BBGKY hierarchy in the kinetic theory of gases.On study leave from the Department of Mathematics, University of Rajshahi, Bangladesh. 相似文献