MATLAB: Fsolve with an evolution parameter

How can I add an evolution parameter into a function in prior to use fsolve?

For example, if my function is

function F = myfun(x)
F2 = [2*x(1) - x(2) - exp(-x(1));
      -x(1) + 2*x(2) - exp(-x(2))];
end

and I can simply use fsolve by this (according to the documentation),

x0 = [-5; -5];
options = optimoptions('fsolve','Display','iter');
[x,fval] = fsolve(@myfun,x0,options)

However, instead of '2' in the second equation, I would like to change it into a parameter a(t),

    F2 = [2*x(1) - x(2) - exp(-x(1));
          -x(1) + a*x(2) - exp(-x(2))];

where the value of a(t) is updated in a loop of 't'

The function now is

function F = myfun(x,a)
F = [2*x(1) - x(2) - exp(-x(1));
      -x(1) + a*x(2) - exp(-x(2))];
end

where I cannot either update 'a' or use the fsolve anymore

Is there any way out without having to write an explicit solver?

Any helps are appreciated,

Mate