@salim-barzani As you know, for consistency I always write ode's and equation to solve without the =0.

Maple itself doesn't have anything; at least ?fuzzy does not return anything. But the application center has four applications to do with fuzzy sets or fuzzy controllers; don't know if this includes fuzzy derivatives.

@salim-barzani Changed signs in ode to match trigh solution. The convert to exp shows Eq 3 can't be right, so I hacked it.

Download T1.mw

@salim-barzani I went through the code making a few changes but with the same result. I didn't check every equation with the paper, but since the final odetest succeeds, it seems everything is working. So I have no idea what you are actually asking, and am not going to spend more time unless you give a very specific question about a particular equation.

Dr.D-feedback2.mw

@salim-barzani I really don't understand what you are asking, but this is my best guess

Dr.D.mw

@salim-barzani I'm don't understand what you are trying to do. See attached for the immediate solution to the error.

A.mw

@salim-barzani You seem to have gone back to using all monomials as before. The paper just says "after arduous calculations". So I don't know what to do here.

@Christopher2222 Yes, the double underscore is just for appearance; I guess you could say "one off". I don't think there is a convention for packages to use one or the other scheme.

@salim-barzani You can convert the answer to explicit forms using allvalues even if solve does not do it.

At first I thought it was a challenge to factor the two numbers given, but the first ends in a 5, so that is definitely too easy. I reread it and I still do not know what exactly you are asking. Would you please clarify.

@salim-barzani Once you have run the loop you know which answers are good, and can do latex or whatever on them later. I don't know why solving only for the a[i] doesn't work. In general you want the same number of variables as equations and if you don't as here then you may be lucky or not. I also don't know why explicit isn't working as it should.

@Christopher2222 Sometimes you want to use the subscript for a purpose, e.g., table index, so you need M[index], but sometimes you don't want the subscript to have any significance and just be part of the name, then M__index is appropriate. For integer indices the subscript is upright, e.g., for M[21], but italic for M__21 so you can see the difference.

@salim-barzani OK, I think you now have acceptable answers.

@janhardo I'm not sure what the problem is; it seems to work as well with f and g?

Using op(0,F) to find the function name seems not to make much sense for arbitrary expressions, but perhaps you only want to use it for functions. I think you should use declare rather than alias if you are using PDEtools. I'm not following what you actually are doing, but maybe this version works as expected?

Download ND.mw

@salim-barzani Isn't putting F1 into H to find u supposed to give a solution to the pde (or perhaps to the linear part?). If so you should check that before moving on to the a[i] part of the problem.