fit with integral function involved

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Daniele Sonaglioni 2021-3-3

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Hello everybody,

i have a problem with mi code. I need to fit this function to my experimental data:

where

and

in which E_1,E_2,T^* and T^' are my fitting parameters and T is my abscissa.

I have a subroutine previously written but i have some problem in insterting the T variable in my script.

Below I show the subroutine i have previosly written (the shape of the function is a bit different):

function y = integralfit(b,Tv,R,nu,T0)
    % % % MAPPING: b(1) = E1,  b(2) = E2,  b(3) = Tstar,  b(4) = Tdot
    
    for k = 1:numel(Tv)
        k3 = @(T) exp(-b(2).*(1./T - 1./b(3))./R);
        K  = @(T) exp(-b(1).*(1./T - 1./b(4))./R);
        y(k) = (b(1)/nu) .* k3(Tv(k)).* K(Tv(k)) .* exp(-(1./nu).*integral(@(T) k3(T).*K(T), T0, Tv(k), 'ArrayValued',1));
    end
end

Here i show my attemp to modify the subroutine:

function y = integralfit(b,Tv,R,nu,T0)
        
    for k = 1:numel(Tv)
        k3 = @(T) exp(-b(1).*(1./T - 1./b(2))./R);
        K  = @(T) exp(-b(3).*(1./T - 1./b(4))./R);
        y(k) =@(T) ((b(1)*K(Tv(k)))./(K(Tv(k))+1).^2).*(K(Tv(k))./nu+b(1)./(R*T.^2)).* exp(-(1./nu).*integral( (k3.*K)./(1+K), T0, Tv(k), 'ArrayValued',1));
    end
end