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khalil20232023

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Where the error in the following code?...

khalil20232023 15 Maple 2016
homework differential-equations duplicate-question
April 15 2023
0 0

alpha1 := .8; alpha2 := .6; eq1 := fracdiff(x(t), t, alpha1)-t^2*x(t)+y(t)-2*t = 0; eq2 := fracdiff(y(t), t, alpha2)-2*z(t)+2*(t+1) = 0; eq3 := z(t)-y(t)-2*t*x(t)+t^4-t-1 = 0; N := 4; x0 := 0; y0 := 0; z0 := 1; XT1 := D[xt](eq1); XT2 := D[xt](eq2); XT3 := D[xt](eq3); XT1[0] := x0; XT2[0] := y0; XT3[0] := z0; for n to N do XT1[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT1))), t); XT2[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT2))), t); XT3[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT3))), t) end do; xseries := add(XT1[n](t)*t^(n*alpha1)/factorial(n*alpha1), n = 0 .. N); yseries := add(XT2[n](t)*t^(n*alpha2)/factorial(n*alpha2), n = 0 .. N); zseries := add(XT3[n](t)*t^(n*alpha2)/factorial(n*alpha2), n = 0 .. N); x_sol := unapply(xseries, t); y_sol := unapply(yseries, t); z_sol := unapply(zseries, t); print(x_sol); print(y_sol); print(z_sol)

proc (t) options operator, arrow; 1.000000000+1.119174954*XT3[1](t)*t^.6+.9076036841*XT3[2](t)*t^1.2+.5964840410*XT3[3](t)*t^1.8+.3354346720*XT3[4](t)*t^2.4 end proc

 (1)

``

Download Ex2_FDAEs.mw

I can not explore the error when I run t...

khalil20232023 15 Maple 2016
homework differential-equations fractional-derivative
April 10 2023
1 0

restart;

Frac_C := proc (expr, a, t, alpha) local ig, m, tau;

m := ceil(alpha);

ig := (t-tau)^(m-alpha-1)*(diff(eval(expr, t = tau), tau$m));

`assuming`([(int(ig, tau = a .. t))/GAMMA(m-alpha)], [a < t]);

end proc;
r := .5;

k := .7;

eq1 := Frac_C(x, 0, t, r)-y(t) = 0;

eq2 := Frac_C(y, 0, t, k)-x(t)-2*t = 0;

eq3 := x(0)-y(1) = 0;

eq4 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x), x = 1)) = 0;

eq5 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x, x), x = 1)) = 0;

eq6 := eval(diff(y(x), x), x = 0)-x(1)-2 = 0;

eq7 := y(0) = 0;

N := 5;

x[c] := [seq(a[i], i = 0 .. N)];

y[c] := [seq(b[i], i = 0 .. N)];

for n to N do

subs([seq(x(i) = x[c][i], i = 0 .. n), seq(y(i) = y[c][i], i = 0 .. n)], {eq1, eq2, eq3, eq4, eq5, eq6, eq7});
soln := solve({eq3, eq4, eq5, eq6, eq7, seq(coeff(lhs(eq), t, j) = 0, eq in {eq1, eq2})}, {a[n+1], b[n+1]});

x[c][n+1] := eval(a[n+1], soln);

y[c][n+1] := eval(b[n+1], soln);

end do;

x[s] := add(x[c][i]*t^(i-1), i = 1 .. N+1);

y[s] := add(y[c][i]*t^(i-1), i = 1 .. N+1);

x[s];

y[s];

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