in this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{ax_n+x_{n-1}}{b+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $a, b$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

In this paper, we use the Mellin-Barnes-Watson method to relate solutions of a certain type $q$-difference equations at $Q=0$ and $Q=\infty$. We consider two special cases; first is equation $K$-theoretic $I$-function quintic, which degree 25; Adams' find extra 20 $Q=0$. The second case fuchsian case, confluent differential cohomological quintic. compute connection matrix study confluence struc...