[Edit: for S, the line

S:= (sqrt(2)/2^k)2*Matrix(M,M, (i,j)-> `if`(`and`(i::odd,j=1) ,-1/(2*i*(i-2)),0)):   

needs the  2 bolded above. Also, the loop you create S in can be discarded, you just need to set M and then the above line does it all]

For C, it's only partly a band matrix, and with many special cases in the first 2x2 block, I'd just make C this way

Download MatrixC.mw

For fractional differentiation in Maple use fracdiff. fracdiff(u(x,t),t,3/2) returns an integral. intsolve solves integral equations but complains this one is not linear, so I'm not sure where to go from here. Perhaps you know some methods for solving these eqns (laplace transforms perhaps?) that you could implement step by step.

Premultiply by the 4x4 matrix with 1's on its reverse diagonal.
 

Download Matrix.mw

The 1 or 2 means differential with respect to the first or second variable, so [2,2] means with respect to the (unnamed) second variable and then again with respect to that variable. The (x,0) means that the second variable is then set to zero. 

Download diff.mw

Download ternary.mw

The variable in LinearSolve means there is a family of solutions, a line, which can be plotted with spacecurve. The planes can be plotted in various ways, e.g. with implicitplot3d

problem.mw

Not sure if I understand what you want. If you right-click and find table properties, you can change the width of the table to be say 50% of the page width. This seems to be respected when you export to .pdf

There is an example on the worksheet of examples referred to on the Explore help page. If I apply it to your example I get

(plot doesn't show here)

Download ExploreODE.mw

As @tomleslie points out, this can be done in Maple with (F@@k)(z0). Note that (F@@0)(z0) returns z0 unlike your routine that returns NULL.

Change your last line to fsolve(ss) and you will get a solution.

You don't have an initial value for v1 or H0. And you need := not = after p0 and q0.

You generated a Matrix A with the RandomMatrix command, and then altered its entries in a loop. But for B, you never declared a Matrix (with, say the Matrix command) and so you ended  with a table by default. So just use B:=Matrix(3,3); before the loop.

You can see individual entries of a table such as W by giving the indexed form, say W[1]. To see the contents of the whole table use eval(W)

Works in Maple 2017.3, so maybe you should update your Maple 2017.

Download solve.mw

This is hard to diagnose without the worksheet, which you can upload with the big green up-arrow.

But the [1] in -1.*HFloat(0.0)[1]' suggests it is a problem with using subscripted variables like i[p](t). If you just want p to look nice as a subscript, use i__p(t) (double underline). Maple doesn't alway handle indexed variables i[p] the same as simple variables. If you change those, I think it will work, but will be easier to diagnose.

The immediate problem is that R:=Rser (which assigns Rser to R) should be R=Rser (which compares the two, in the context of an if statement). But also jthen should be then and notice that both R and Rser are locals that do not have values when you do the test in the if statement. For future reference, upload your worksheet using the big green up arrow to make it easier for others to diagnose your problems.