@mmcdara I'm update my answer.

@perr7 

1.I don't have Maple 17.

2.I used Maple 2021.

3.I changed  sum to add function.

See atached file.

Calculation_ver_2.mw

Update 03.01.2022

I also need a lot of things. Above paper is not free.

Try with maybe works in yours version:

evalf(Int(abs(u(x) - P__2), x = -1 .. 1, method = _CCquad));

?

I would like to see significant improvement of solving analyticaly(symbolicaly):

1.Integrals.

2.Sums.

3.Product.

4.Integral Transfrom and Inverse like Laplace,Fourier,Mellin,Hankel,Hilbert.

5.Sum Transfrom and Inverse like Ztrans.

6. Linear and nonlinear integral equations.

See, for example, integrals the comparison here.

I would like to see significant improvement of solving numerically:

1.A update a pdsolve numerically higher-order multidimensional partial differential equations.

2.A update a pdsolve numerically to solve elliptic PDEs, but now can't handle.

Maybe this helps:

https://www.mapleprimes.com/questions/228656-How-Do-I-Solve-Fractional-Differential

@KIm Gaeun 

Paste Maple code not a picture. What definition is m(s) ?

@nidojan 

@AHSAN 

% - gives the last result generated.

@AHSAN 

For : k=2,lambda=1.

first_ode.mw

@AHSAN 

Try:

h := k - (k - 1)*x;
lambda := k/(1 + k);
ode := diff(p(x), x) = 6/h^2 - 12*lambda/h^3;
bc := p(0) = 0, p(1) = 0;
simplify(dsolve({bc, ode}, p(x)));
is(eval(p(x), %) = 6*(h - 1)*(h - k)/(h^2*(-k^2 + 1)));

@Thomas Richard 

 When can we expect implementation for fractional ODE in Maple?.It is possible in the very near future or not at all?

@Scot Gould 

Try:

(diff(sum(x^n, n = 0 .. infinity), x) assuming (-1 < x < 1));

or:

diff(sum(x^n, n = 0 .. infinity, formal), x);

@Sradharam 

Not so easy to solve, a nonliner ode with power series solution: See

Maybe his helps  see

Series.mw

@Sradharam 

With  infinite series solution I don't know how to it.

I solved with another method by Homotopy perturbation.If you what  to, see attached file.

HOMOTOPY.mw