The existence problem of logarithmic Borel exceptional values for Jackson difference operators and Askey-Wilson difference operators of meromorphic functions is studied by using Nevanlinna theory of meromorphic functions,and the relationships concerning logarithmic Borel exceptional values between nonconstant meromorphic functions f with finite logarithmic order and the of Jackson difference operator(D)qfor Askey-Wilson difference operator(D)AW fare investigated.We proved:let f be a nonconstant meromorphic function with finite logarithmic order,q ∈ C satisfying 0＜|q|＜1.n∈ N,such that (D)nqf(≡)0.Then for a ∈C and b ∈(C)\{0},limsup log+{n(r,a,f)+(r,b,(D)nqf)/loglogr}=ρlog-1.With regard to Askey-Wilson difference operator (D)AWf,we also obtain the same results.
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