fitting multi data sets with shared variables with same fitting equation

Dear Matlab expert: I have a set of data F which depend on two variable field size (L) and thickness (w). I would to fit F(w,L) with the following equation:

F(w,L) = A(L) + B(L) · C(L)^w where; A, B and C are third-order polynomial fitting parameters(i.e. A=A0+A1*L+A2*L^2+A3*L^3); how I can find (A0,A1,A2,A3), (B0,B1,B2,B3) and (C0,C1,C2,C3) fitting parameters using matlab.

Many thanks in advance.