Determining coefficient and fractional derivatives of equation using fminsearch

Hi everyone,

I am new to Matlab and I am unsure on the inbuilt function fminsearch to solve the parameters within this equation.

I have the date for y and all x. I am trying to use fminsearch to look for values of C and the values of the fractional derivatives. The goal is to minimize MSE which is given by:

[Sulaymon Eshkabilov]

Can you show what you have done so far? One small advice is that you can start with:

doc fminsearch

That shows a good documentation how to employ fminsearch() and write function files or function handles.

[Yew Seng Tan]

Hi Sulaymon Eshkabilov ,

I am actually trying to reproduce the results of the research paper entitled "Fractional Calculus in Economic Growth Modeling The Portuguese case". As of now, I am using the alpha values of Fractional (3) shown below:

This is the code that I used though not very accurate in terms of the equation writing, I have used Caputo derivatives to obtain the derivative values via matlab.

% Original Equation: Y=c(1)*X1+c(2)*X2+c(3)*X3+c(4)*x4+c(5)*X5+c(6)*X6+c(7)*X7+c(8)*X8+c(9)*X9
% Variable Matrix:
Y=GDP*10^11;
Y = Y(:);
X = [X1 X2 X3 X4 X5 X6 X7 X8 X9];
X = [X1(:) X2(:) X3(:) X4(:) X5(:) X6(:) X7(:) X8(:) X9(:)];
% Parameters: c1=c(1) c2=c(2) c3=c(3) cn=c(n) where n={1,2,3,4,5,6,7,8,9}
Yfcn=@(c,X) X(:,1).*c(1)+X(:,2).*c(2)+X(:,3).*c(3)+X(:,4).*c(4)+X(:,5).*c(5)+X(:,6).*c(6)+X(:,7).*c(7)+X(:,8).*c(8)+X(:,9).*c(9)
SSECF=@(c) sum((Y - Yfcn(c,X)).^2)/53;
c0=-100*1e10+(2*100*1e10).*rand(1,9);             % Initial Parameter Estimates (-100*10^10,100*10^10)
%c0=[-6.614*1e4, 8.535*1e5, 8.835*1e2, 9.299*1e8, -24.469*10^-2, 9.159*10^-1, 3.037, -9.655*10^-3, -3.869*10^-2];
options = optimset('MaxFunEvals', 1E7, 'MaxIter', 1E7);
[c,SSE] = fminsearch(SSECF,c0,options);

I am trying to get values as close to these values:

The problem is I am trying to find a way to obtain both alpha and coefficients that are as close to the values shown in the table via fminsearch similar to what the research paper uses.