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Spectrum behavior for the nonlinear fractional point reactor kinetics model
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作者 Ahmed E.Aboanber Abdallah A.Nahla A.A.Hemeda 《Nuclear Science and Techniques》 SCIE CAS CSCD 2018年第1期96-109,共14页
The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density int... The nonlinear fractional point reactor kinetics equation in the presence of Newtonian temperature reactivity feedback with a multi-group of delayed neutrons,which describes the spectrum behavior of neutron density into the homogenous nuclear reactors, is developed. This system is one of the most important stiff coupled nonlinear fractional differentials for nuclear reactor dynamics. The generalization of Taylor's formula that involves Caputo fractional derivatives is developed in an attempt to overcome the difficulty of the stiffness of the nonlinear fractional differential model. Moreover, the general fractional derivatives are calculated analytically throughout this work. Furthermore, the local and global estimated errors were analyzed, which suggest that the error quantification should take into account the possible grow in time of the error. This observation provides a motivation for going beyond more classical local-in-time concepts of error(local truncation error). The neutron density response with time is analyzed for the anomalous diffusion, sub-diffusion, and super-diffusion processes. 展开更多
关键词 Nonlinear fractional Generalized taylors FORMULA POINT kinetics MULTI-GROUP DELAYED neutrons Temperature feedback REACTIVITY
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分数微积分下Taylor公式的一种推广
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作者 孙贺琦 《三明学院学报》 2008年第4期374-376,共3页
基于分数微积分理论,将分析学中的Taylor级数和Taylor公式推广于f=(x-a)νg,g∈Cω(I)型函数,并对得到的分数幂级数的系数关系和余项作了分析.
关键词 分数微积分 分数幂级数 taylor公式 余项分析
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An Approach to Differential Geometry of Fractional Order via Modified Riemann-Liouville Derivative 被引量:1
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作者 Guy JUMARIE 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第9期1741-1768,共28页
In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one (Jumarie) has proposed rece... In order to cope with some difficulties due to the fact that the derivative of a constant is not zero with the commonly accepted Riemann-Liouville definition of fractional derivative, one (Jumarie) has proposed recently an alternative referred to as (local) modified Riemann-Liouville definition, which directly, provides a Taylor's series of fractional order for non differentiable functions. We examine here in which way this calculus can be used as a framework for a differential geometry of fractional or- der. One will examine successively implicit function, manifold, length of curves, radius of curvature, Christoffel coefficients, velocity, acceleration. One outlines the application of this framework to La- grange optimization in mechanics, and one concludes with some considerations on a possible fractional extension of the pseudo-geodesic of thespecial relativity and of the Lorentz transformation. 展开更多
关键词 fractional calculus modified Riemann-Liouville derivative fractional taylor's series fractional manifold fractional geodesic fractional mechanics Lorentz transformation
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有理既约真分式化为部分分式的又一方法
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作者 王富贵 《辽宁工学院学报》 1995年第4期79-81,共3页
利用多项式函数的泰勒公式,给出了把有理既约真分式化为部分分式的一种方法。
关键词 有理既约真分式 部分分式 泰勒公式 多项式函数
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