In[]:=
Clear["`*"];​​​​u[x_,t_]:=t*a0[t];(*a0(t)isunknownfunction*)​​
1
Gamma[2-α]
Integrate[D[u[x,z],{z,2}]*
1-α
(t-z)
,{z,0,t},Assumptions1<α<2]​​
Out[]=
Integrate[
1-α
(t-z)
(2
′
a0
[z]+z
′′
a0
[z]),{z,0,t},Assumptions1<α<2]
Gamma[2-α]