I have now no issues with delta nor its derivative. BTW p is transition probability, p(t = 0) = delta.You need delta or actually its derivative?
the Q can I write FPE in verry nice compact form and what are the advantages
p_t = (A (B p_x))_x
it's just another PDE.
You should be able to always transform to:
p_t = (A (B p_x))_x + V(x) p
for all 1D problems, as all [$]D = 1[$] diffusion problems involve self-adjoint operators in a weighted L^2 space.
(See footnote 3, Ch. 2 in my Vol II book).
Doesn't work in [$] D \ge 2[$], where the "generic" diffusion operator is non-self-adjoint.