@Alfred_F 

thank you

@nm 

Thank you 

How can I get a real  value and not complex solution 

@Christian Wolinski 

Thank you 
can we display the chain of prime ideals which confirm that the height of ideal

@dharr 

thank you, 

I tried to simplify the equations and avoid proc 
I get another error

 last.mw

thank you for your time

@Axel Vogt 

thank you for your time. 

@dharr 

can we use this formula to simplify the output of y[i]

@Axel Vogt 

Good formula, so this formula can be used to calculate each y[i], how can I say to maple substitute this formula to compute each y[i]

@Axel Vogt 

Can Maple compute the formula?

@Axel Vogt 

Please see lemma 3 in 
file:///D:/Download_documents/F1.pdf

@acer 

Thank you for your time, 
I simplied the code, I write only one line, how evaluate the following integral 

one_integral_compute.mw

thank you

@acer 
I added ''continuous '' as option but does not return the appropriate answer

Frac_D := proc (f, psi, alpha, a, x) `assuming`([(int((diff(psi(t), t))*(psi(x)-psi(t))^(alpha-1)*f(t), t = a .. x, continuous))/GAMMA(alpha)], [0 < alpha, alpha <= 1, 0 < x, x <= diff(psi(x), x) and diff(psi(x), x) <> 0]) end proc

@acer 

Yes, I agree. Thank you. 
This can be used to compute y[0] 

Please what about y[i]

@dharr 

thank you

@mmcdara 

Please, how can I select from your code only the solution that verify some assymption ( positive parameter ) as added in the code 
Stab_sssymption.mw

Thank you for your answer, 
You say you beleave that this can be done more simply, can you propose another idea