## 305 Reputation

7 years, 286 days

## Thanks @vv. What about  ...

Thanks @vv.

What about  L-2 error norm ?

## Thanks, dear @Carl Love, it's a...

Thanks, dear @Carl Love, it's a brilliant solution.

I want to change the question a little bit.

Let's select as follows:

=

where

is a real number.

In fact; it is a generalization of the question in the post. If we select , it transforms to original post.

How to get an explicit formula?

I wrote a code as follows by adapting your code above:

Although I waited a lot, Maple did not give any results. (I think we need more assumptions )

```restart:
interface(showassumed= 0):

assume(n::posint, j::nonnegint, j <= n, T > 0, alpha > 0,rho::realcons);
h:= T/n:

psi:= t->
local i:= op(procname);
convert(
if i=0 then piecewise(t<0, 0, t<h, 1-t/h)
elif i=n then piecewise(t < T-h, 0, 1-(T-t)/h)
else
piecewise(
t < (i-1)*h, 0,
t < i*h,     t/h-(i-1),
t < (i+1)*h, (i+1)-t/h
)
fi,
Heaviside
):

g:= proc()
local i,j,rho,t;
(i,j):= op(procname);
simplify(
int(t^(rho)*((j*h)^(rho+1)-t^(rho+1))^(alpha-1)*psi[i](t), t= 0..j*h)*(rho+1)^(1-alpha)/GAMMA(alpha)
)
end proc
:
g[0,j]() assuming additionally, j > 0 ;

g[j,j]() assuming additionally, j > 0;

g[i,j]() assuming i::posint, additionally, i < j;

```

## Thanks, dear @Kitonum,I use `Standa...

Thanks, dear @Kitonum,

I use `Standard Worksheet Interface, Maple 2020.2, Windows 10, November 11 2020 Build ID 1502365`, everything is the same as yours.

Yes, your solution way is an alternative, but in fact, everybody wants/hopes to accomplish this by using the plotplots:-textplotplottools:-rectangle  commands etc.

## Thanks for your interesr @dharr,if ...

Thanks for your interest @dharr,

if alpha=1;

`fracdiff(t, t,alpha)`

gives 1. But it doesn't appear in the figure.

if alpha=0,

`fracdiff(t, t,alpha)`

gives t. But it doesn't appear in the figure, also.

## You are right dear @acer, I will t...

You are right dear @acer,

I will try to achieve it.

Thanks.

## Thanks, @acer,In fact, I don't ...

Thanks, @acer,

In fact, I don't mean the location of the legends in my last question.

In your code, since the lines in the figure include the solid circles, the legends must include also them. I marked one of them on the following figure. How can we achieve this?

## Dear @acer, Your solution is good....

Dear @acer,

Your solution is good.

But, while the lines includes solid circles, but the circles doesn't appear in the legends. Can we solve this?

On the other hand, ı know Maple has some options instead of circles. But is it possible as follows?

## @Thomas Richard, Oh yes, you are right....

Oh yes, you are right. I edited the post.

## @vv  You can find the Ma...

You can find the Maple_code.mw for , P(1), P(2).

For N=1, you are right may be  int(Psi(s), s=0..t) <>P(1)*Psi(t).

But this is a numerical approximation. When N increases, we get more exact results. I tested it in the Maple_code.mw

## Thanks for your interest Dear @vv&n...

Thanks for your interest Dear @vv

But for N=1,  Psi(t)  is not equal to zero. Why do you think it's zero?  (I don't understand exactly)

Meanwhile, this method is a kind of wavelet method, and it's commonly used.

## Dear Prof. @Carl Love,I explained s...

Dear Prof. @Carl Love,

I explained some more below.

The following is the thing which I want to write a procedure in my question post.

IN FACT;

I want to check the below solution algorithm for Differential Equations by Maple. This is a simple example. But I have more complicated examples. So I want to use MAPLE for the symbolic operations below.

This is one part of the mey method. If we write a Maple code for this part, I hope so I can handle the rest.

## Thanks for your interest ear @Carl ...

Thanks for your interest dear @Carl Love.

P(1), P(2) are NxN matrix functions.
For N:=2, they are as follows, respectively.

```P(1):=
Matrix(2, 2, [[0.5, 0.2886751345229591], [-0.216506351, 0.]]);

P(2):=Matrix(2, 2, [[0.16666666666666669, 0.14433756726147953], [-0.1082531755, -0.08333333333333333]]);```

## A question...

Dear @Mariusz Iwaniuk,

Thanks for your valuable response.

I have a question about the fractional differential equation.

https://data.mendeley.com/datasets/dn82gkvf4f/1

I write the following code, but I get an error when I run the code.
Could you help me, please?
Best regards.

QUESTION:
for 0<x<1, and alpha=1,
exact Solution of the following equation is u(x,t)= 3*exp(t)/(1-3+3*exp(t)):
-------
CODE:
eq:=diff(u(x,t),t\$alpha)-diff(u(x,t),x,x)-u(x,t)*(1-u(x,t))=0;
IC:=[u(x,0)=3];
-------
But the error is  "Error, (in SeparateOperator) improper op or subscript selector |InitialInterface.mpl:257| "

And I want to also run the code for alpha=0.5 with suitable initial/boundary condition.

## Dear @acer , thanks for your i...

Dear @acer , thanks for your interest. But I think I was misunderstood.

I want to mean that

2d graphics:
for alpha=0.3,  when we run the code, we get a graphics of function UU(0.5,t)

and after restarting the code

for alpha=1 when we run the code again, we get a graphic of function UU(0.5,t).

So, I want to display these two graphs together in one graph (2d).

And also for 3d graphics:

for alpha=0.3,  when we run the code, we get a graphics of function UU(x,t)

and after restarting the code

for alpha=1 when we run the code again, we get a graphic of function UU(x,t).

So, I want to display these two graphs together in one graph (3d).

## Dear @tomleslie, thanks for your in...

Dear @tomleslie, thanks for your interest. But I think I was misunderstood.

I want to mean that

2d graphics:
for alpha=0.3,  when we run the code, we get a graphics of function UU(0.5,t)

and after restarting the code

for alpha=1 when we run the code again, we get a graphic of function UU(0.5,t).

So, I want to display these two graphs together in one graph (2d).

3d graphics:

for alpha=0.3,  when we run the code, we get a graphics of function UU(x,t)

and after restarting the code

for alpha=1 when we run the code again, we get a graphic of function UU(x,t).

So, I want to display these two graphs together in one graph (3d).

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