a = 1.1; b = 0.02; c = 0.035; d = 1.0; k = 0.3; e = 0.5; f = 0.2; \
\[Alpha] = 0.98; h = 1; n = 1 + t; U[0] = 0.3; V[0] = 0.2; W[0] = 0.5;
Subscript[S, 1][
t_] := (t - 1)/\[Alpha] ((n + 1) - (t + 1))^\[Alpha] - (t +
1)/\[Alpha] ((n + 1) - (t + 1))^\[Alpha] -
1/(\[Alpha] (\[Alpha] + 1)) ((n + 1) - (t + 1))^(\[Alpha] -
1) - ((t -
1)/\[Alpha] ((n + 1) - (t))^\[Alpha] - (t)/\[Alpha] ((n +
1) - (t))^\[Alpha] -
1/(\[Alpha] (\[Alpha] + 1)) ((n + 1) - (t))^(\[Alpha] - 1));
Subscript[S, 2][
t_] := (t)/\[Alpha] ((n + 1) - (t + 1))^\[Alpha] - (t +
1)/\[Alpha] ((n + 1) - (t + 1))^\[Alpha] -
1/(\[Alpha] (\[Alpha] + 1)) ((n + 1) - (t + 1))^(\[Alpha] - 1) +
1/(\[Alpha] (\[Alpha] + 1)) ((n + 1) - (t))^(\[Alpha] - 1);
Ut = U[t] ==
U[0] + 1/
Gamma[\[Alpha]] ((U[t] c d (V[t])^a - f c V[t] (U[t])^a)/
h Subscript[S, 1][
t] - (b (
U[t - 1] c d V[t - 1]^a - f c V[t - 1] (U[t - 1])^a))/
h Subscript[S, 2][t]);
Vt = V[t] ==
V[0] + 1/
Gamma[\[Alpha]] ((c f (1 - 2 V[t] - W[t]) (U[t])^a +
d c (V[t])^a U[t])/
h Subscript[S, 1][
t] - (c f (1 - 2 V[t - 1] - W[t - 1]) (U[t - 1])^a +
d c (V[t - 1])^a U[t - 1])/h Subscript[S, 2][t]);
Wt = W[t] ==
W[0] + 1/
Gamma[\[Alpha]] ((d f (1 - V[t] - W[t]) (U[t])^a)/
h Subscript[S, 1][
t] - (d f (1 - V[t - 1] - W[t - 1]) (U[t - 1])^a)/
h Subscript[S, 2][t]);
