I can't see your PDEs, but if you have just a single spatial dimension you should be able to rewrite the system as coupled ODEs.
Again I cant see your equations, but I think that as long as at least one of the equations in the system has a nonzero laplacian then pde toolbox should work. You'll need to define your coefficient functions appropriately (c,a,f&d, c in this case will be zero for the first order PDE).