%《灰色系統理論及其應用》第7版 劉思峰 P193 9.3基于Captuo模型分數階導數的灰色模型 %實現 ，采用例9.2.1的數據完成分析clear all,clc,close all %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %求X0的p階差分，相當于 %先進行1－p階（=1-0.1=0.9）累加，得到累加序列X1p,再進行1階累減。X0=[247.839,273.021,289.014,285.208,288.818,297.078];p=0.98;p1=1-p; %-代表分數階X1p=[];for k = 1:length(X0)s=0;for i=1:k product=1;if i<kfor j=0:(k-i-1)product=product*(p1+j);ends=s+ product/factorial(k-i)*X0(i); elses=s+X0(k);endendX1p=[X1p,s];end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 對累加序列X1p作1次累減，得到X0的p階差分X0_p X1p_1=[0 X1p(1:end-1)]; X0_p=X1p-X1p_1 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 計算發展系數－a, 灰色作用量b % Y=X0_p(2:end)'; Z=(X0(1:end-1)+X0(2:end))/2; B=[-Z' ones(length(X0)-1,1)]; ab=inv(B'*B)*B'*Y; a=ab(1) b=ab(2) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % X0y=[]; syms n; for k=1:length(X0)X0y=[X0y (X0(1)-b/a)*double(symsum((-a*k^p)^n/gamma(p*n+1),n,0,Inf))+b/a]; end X0y

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