[PDF] Top 20 Some results on q difference equations

... where the right-hand side is rational in both arguments, has been widely studied during the last decades; see, e.g., [–]. Gundersen et al. [] considered the order of growth of mero- morphic solutions of (.), from ... See full document

... fractional q-difference calculus had its origin in the works by Al-Salam [] and Agarwal ...fractional q-difference cal- culus were made, specifically, q-analogues of the integral and differential ... See full document

... N}. Note that the operator A : U → PC is continuous and completely continuous. From the choice of U , there is no x ∈ ∂ U such that x = λ Ax for some λ ∈ (, ). Consequently, by the nonlinear alternative of ... See full document

... on q-difference calculus or quantum calculus dates back to Jackson’s papers [, ], while a systematic treatment of the subject can be found in [, ...For some recent existence results on ... See full document

... of some types of systems of higher-order complex difference equations are ...investigated. Some new results are ...complex q-difference equations, and we obtain some new ... See full document

... with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference ...equations. Some applications are made of some fixed ... See full document

... present some existence results for the problem ...present some basic material that we need in the sequel and ...main results of the paper. Some illustrative examples are also ... See full document

... the results of this paper, we can obtain some special new results for q-difference ...our results correspond to the ones for second-order q-difference ... See full document

... of some linear difference equations. We obtain some new results on the growth of meromorphic solutions when most coefficients in such equations are meromorphic functions, which are ... See full document

... description by a Newton polygon. It is important to stress that this approach is specific to the q-difference case. Namely, such a direct procedure for producing two different Gevrey levels in the differential case ... See full document

... and results in Nevanlinna’s value distribution theory of meromorphic functions such as the characteristic function Tr, f , proximity function mr, f , counting function Nr, f, the first and second main theorems ... See full document

... generalized q-Taylor’s formula involving Caputo fractional ...generalized q-differential transform and its inverse and establish some basic properties for this ...solve some linear and ... See full document

... The paper is organized as follows. In Sect. 2, we recall some basic concepts on q-calculus and present some properties and lemmas that will be used in the proofs of our results. Section 3 is ... See full document

... In this paper, we discussed the problem of nonlocal value for nonlinear fractional q-difference equation. The classical tools of fixed point theorems such as Krasnoselskii’s theorem and Banach’s contraction ... See full document

... complex q-shift difference equations with meromorphic solutions from the point of view of Nevanlinna ...theory. Some results obtained in this paper improve and extend the previous theorems ... See full document

... difference equations and prove a number of ...under some special cases and provide some examples to show that the answer to a question of Laine and Yang is not always ... See full document

... ference equations with positive coefficients, which were studied by Chatzarakis et ...the results of the paper imply oscillation while previously known results ... See full document

... complex q-difference equations (resp. differential- q-difference equations) instead of complex difference equation ...involved equations are more general than ...Riccati q-difference ... See full document

... Motivated by the previously mentioned works, we will consider the existence of solu- tions of q-fractional p-Laplacian BVP with two-point boundary conditions. The main dif- ficulty is that, for p = , it is ... See full document

... function α IM, recently Wang has generalized Gundersen and Yang’s results, see []. In this paper, we consider the uniqueness of entire functions sharing a small function with their linear difference and ... See full document