# Why is an empty plot produced?

I am trying to plot the values of the functions f[x] and der[x], but I am getting an empty plot. I am new to both Mathematica and simulation. Can anyone please help me.

Manipulate[
fu[alfa],
{{alfa, 1, "α"}, 0, 1, 0.001, Appearance ->"Labeled"},
Initialization :> (
fu[alfa_] :=
Module[{α, f, der},
α = alfa;
f[x_] = Exp[x];
der[x_] = Sum[((t)^(k) x^(-α))/Gamma[k + 1 - α], {k, 0, ∞}];
Plot[{f[x],der[x]}, {x, 1, 1.5},
AxesLabel ->
{Style["x", Italic],
Row[{Style["f", Italic], "(", Style["x", Italic], ")"}]},
ImageSize -> {300, 200},
ImagePadding -> {{35, 20}, {20, 20}},
PlotStyle -> Thick]])]

• This code cannot be copied into a notebook in its current state because of syntax errors. For example, [Alpha] is not a valid symbol name. – Sjoerd Smit Jun 24 at 8:20
• what is the value of t in Sum[((t)^{k)...]? – kglr Jun 24 at 8:36
• When ever you can't get a complicated piece of code to work, a good strategy is to start first with something that does work, a simple plot, then add one component to it, get it working, then add another and slowly build it back up until you add a piece that causes it to fail then focus your attention on getting that single piece to work. – Dominic Jun 24 at 10:25

There are quite a few programming errors in your code. Probably the most deadly one is not taking into account that der depends on three parameters, x, alfa and t.

Here is a rewrite of your code that produced a plot that can be manipulated. Note, because the evaluation of der is time consuming, response to moving the sliders is rather sluggish.

Clear[f, der]
f[x_] := Exp[x]
der[x_, α_, t_] :=  Sum[t^(k) x^(-α)/Gamma[k + 1 - α], {k, 0, ∞}]

Manipulate[
Plot[{f[x], der[x, alfa, t]}, {x, 1, 1.5},
PlotRange -> {0, 5},
PlotStyle -> Thick,
AxesLabel ->
{Style["x", Italic],
Row[{Style["f", Italic], "(", Style["x", Italic], ")"}]},
ImageSize -> {300, 200},
ImagePadding -> {{35, 20}, {20, 20}}],
{{alfa, 1, "α"}, 0, 1, 0.01, Appearance -> "Labeled"},
{{t, .2}, 0, 1, 0.01, Appearance -> "Labeled"}] • Thank you for your comments – vicky Jun 26 at 7:22