Probably some parameter name doesn't have a value, but if you upload your worksheet with the green up arrow, someone can help you diagnose it.

@TeyhaNeedHelp Use * to enter multiplication, and give values to all parameters.

dsolve.mw

@Mohamed19 If you want something for general _k1, _k3, I don't think you'll get it, since any formula with an unspecified order of differentiation will be hard to deal with. If you use specific _k1,_k3, then you can evaluate and then convert. You can try the general case with convert.

I tried a few conversions, such as convert(  ,binomial) without success, but you could try some others.

@Adam Ledger In windows you can right-click on the .dll and choose properties. There is some information there, which may or may not have the authors etc; that depends on the .dll author.

@Mohamed19 I don't understand. Can you give an example of what you want as an answer.

@Mohamed19 It was unclear what your notation meant, and so I made a guess. Now it is unclear what form you want the answer in, so you will need to give more details of what you are looking for.

I answered this in the other thread https://www.mapleprimes.com/questions/228082-Derivative-Of-BesselJalpha-Sqrtu2v22uvcosphi but you want a sum form. You will need to specify the problem more clearly because your notation above is not clear and it is also not clear what form you really want.

@Mohamed19 I'm assuming the arguments are to be derivative of increasing order. Need to have fixed values of _k1 and _k3. Maybe something like:
 

Download Bell.mw

@Zeineb I suggest you set up your conjecture as a Maple sum, and see if Maple can simplify to zero under the appropriate assumptions.

The code you copy-pasted earlier worked OK as I already showed. Now you have edited that out of your question and are asking something else that is not clear. Suggest you upload your worksheet - use the large green uparrow to load the worksheet with the problem and someone can take a look at it.

@mehdi jafari I agree that it is not in general, but it is if tau=0 and sqrt(sigma1^2) = sigma1, i.e., if sigma1 is positive, which is an important case. 

Suggest you upload your worksheet using the large green up-arrow. Then it will be easier for someone to diagnose.

@arshl If you just want to solve the pde with the given initial and boundary conditions, then laplace/fourier is not the way I would go in this case and I do not know how to do this. Maple's pdsolve uses many methods that could help you solve it without transforms.

For the initial condition, you need to pay attention to @Rouben Rostamian's use of Heaviside, and then you can get the right result:
fourier(Heaviside(x)*(1-exp(-x/sqrt(2))),x,omega);

@arshl You have incorrectly factored out u from diff(u(x,t)*diff(u(x,t),x),x). But in any case, finding laplace/fourier transforms of products such as u(x,t)*diff(u(x,t),x,x) or (diff(u(x,t),x,x)^2 is problematic, and Maple is not succeeding here.

@Carl Love Yes, that was careless. I redid with Laplace, but last term might still have a problem. Not sure what assumptions are required.