In this paper, we deduce the Green’s function for a ν-th order, 1 < ν ≤ 2, discrete fractional boundary value problem with boundary conditions of the type αy(ν−2)−β∆y(ν−2) = 0, γy(ν+ b)+δ∆y(ν+ b) = 0, for α, β, γ, δ ≥ 0 and αγ+αδ+βγ 6= 0. This extends and generalizes the results of some recent papers. We then show that this Green’s function satisfies a positivity property. From this we deduce a...

A function f(z) is called meromorphic, if it is analytic in the complex plane except at poles. It is assumed that the reader is familiar with the standard symbols and fundamental results of Nevanlinna theory such as the characteristic function T(r, f), and proximity function m(r, f), counting function N(r, f) (see [1, 2]). In addition we use S(r, f) denotes any quantity that satisfies the condi...

It is shown that, if f is a meromorphic function of order zero and q ∈ C, then m „ r, f(qz) f(z) « = o(T (r, f)) (‡) for all r on a set of logarithmic density 1. The remainder of the paper consist of applications of identity (‡) to the study of value distribution of zero-order meromorphic functions, and, in particular, zero-order meromorphic solutions of q-difference equations. The results obta...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Second-order hyperbolic equation Difference scheme Unconditionally stable Stability Initial-value problem Variable...