【摘要】 从分数演算基本的G-L定义出发,引出G-L数值算法中加权系数——G-L加权系数与广义二项式系数之间的关系,进而通过Γ函数来求解G-L加权系数.而后用加权系数的参数构建一个二维平面,使这些参数由整数域拓展到整个实数域,实现了分数演算中加权系数和对应二项式系数的推广.最后利用Matlab语言编程实现,为分数演算的数值计算提供方便、快捷的工具.更多还原

【Abstract】 Start with the Grunwald-Letnikov definition(G-L definition) of the fractional calculus,the relationship between the weight coefficients of the G-L numerical algorithm and the generalized binomial coefficents is introduced.And then,the G-L weight coefficent is obtained by using the gamma function in Matlab.A two-dimensional plane of the G-L weight coefficient and a two-dimensional plane of the generalized binomial coefficient are presented in this paper.Finally,a method how to compute the weight coefficent is given in MATLAB,which is convenient to numerical approximate the fractioanl calculus.更多还原