Arrhenius equation - fitting reaction model and rate constant without toolbox

I have this reaction model with experimental values of rate of conversion (da_dT_scaled_cutE), conversion (a_i_scaled_cutE(:,1)) and temperature (T_int_cutE)

I know the activation energy Ea. Now I'm trying to to fit the rate constant A and reaction model parameters m,n in Matlab. I have fitted A, m, n by non-linear solver in Excel already so I know the rate constant A is order of 1e23.

When I use lsqnonlin function with initial rate constant of 6e23, I get ok fit to the data. However, when I change the initial rate constant to 6e20, no solution is found. The reason is probably that the step change in iterations is very small. That is not the case in Excel non-linear solver which converges. Can I set up the rate constant fitting on vector from 1e8 - 1e25?

par_init = [5 -1 6]; % A n m
amplifier = 1;
%opt = optimoptions('lsqnonlin','DiffMinChange',0.2);
fun=@(par) amplifier*(da_dT_scaled_cutE - ((a_i_scaled_cutE(:,1).^par(2)).*((1 - a_i_scaled_cutE(:,1)).^par(1))).*par(3)*1e23./beta(1).*exp((-Ea(3)*1000)./(T_int_cutE*R)));
[x,resnorm,residual,exitflag]=lsqnonlin(fun,par_init); % non-linear fitting
n=x(1)
m=x(2)
AA=x(3)*1e23

Find the full code in the attachment (line 185).