I'm trying to solve numerically this system of non linear DEs and there's some trouble with the numerical solution of the last differential equation, because while running the last line of the code that uses

`ParametricNDSolveValue` appears the followin message ParametricNDSolveValue::pdvar: Dependent variables {G,F[t,a,b]} cannot depend on parameters {a,b}.

I'm not quite sure about the evaluation in the F function but I tried. Here's the code:

t0 = 7;
u0 = 1.0;
v0 = -0.5;
z0 = Sin[t0];
sol = ParametricNDSolveValue[{
    u'[x] == -Log[10] (-u[x] + a v[x]),
    v'[x] == -Log[10] (u[x] - (a w[x])^2),
    w'[x] == -Log[10] (w[x] (1 + a) - Cos[x]),
    z'[x] == -Log[10] (4 a Sin[x]),
    u[7] == u0, v[7] == v0, w[7] == w0, z[7] == z0}, {u, v, w, z}, {x,
     7, -2}, {a}, MaxSteps -> Infinity];
dynsys[x_?NumericQ, a_?NumericQ] := sol[a][x];
x[t_] := Log[1 + t]/Log[10];
F[t_?NumericQ, a_, ?NumericQ, b_?NumericQ] := 
  Sqrt[(b (1 + t)^3)/(
   1 - u[x[t]]^2 - v[x[t]]^2 - w[x[t]]^2 - z[x[t]]^2)] /. 
   dynsys[x[t], a][[1]];
Gsol = ParametricNDSolveValue[{G'[t]/(1 + t) - G[t]/(1 + t)^2 - 1/
      F[t, a, b] == 0, G[0] == 0}, {G}, {t, 0, 3}, {a, b}, 
   MaxSteps -> Infinity];