Is the output the last iteration or does it output the initial conditions?
It is the last iteration, as you can easily test, .e.g.,
fsolve( @(x) x^2+1,10 )
Essentially, if no solution exists, fsolve can be thought of as a least squares solver.
Also, is there a way when no solution has been found to tell it to output nothing
No, but there is no reason why your code can't do its own post-assessment of the result after fsolve completes.
