[PDF] Top 20 Oscillatory behavior of solutions of certain fractional difference equations

... If there exist positive sequences β , λ such that (11) and (12) hold, then Eq. (1) is oscillatory. Proof Suppose to the contrary that x(t) is a non-oscillatory solution of (1). Then, without loss of ... See full document

... Since we are interested in the oscillatory behavior of solutions of (.) and (.) near infinity, we assume throughout this paper that our time scale is unbounded above. An excellent introduction of ... See full document

... nonlinear difference equation was studied intensively by ...of oscillatory behavior of solutions of nonlinear neutral delay difference ...delay difference equation of the form ∆ ... See full document

... The oscillatory and asymptotic behavior results for a class of third-order nonlinear neutral dynamic equations on time scales are ...dynamic equations of the type considered ... See full document

... the oscillatory behaviors of solutions of vari- ous equations, including differential equations, fractional differential equations, difference equations, fractional ... See full document

... the oscillatory behavior of solutions of fractional differ- ential equation has been a hot topic and some results have been ...the oscillatory behavior of fractional ... See full document

... of difference equations and their applications have been receiving intensive attention in the last few decades, see for example [1, 2, 4], and the references cited ...of oscillatory behavior ... See full document

... Differential equations with maximum arise naturally when solving practical and phe- nomenon problems, in particular, in those which appear in the study of systems with auto- matic regulation and automatic control ... See full document

... all solutions of ...asymptotic behavior, one being asymptotic to ( ∞ , 0) and the other being asymptotic to (0, ∞ ...qualitative behavior at least in the region S 1 ∪ S 2 ... See full document

... differential equations and difference equations has been developed rapidly in the last decades, and there have been many results on the oscillatory behavior of integer-order differential ... See full document

... constant solutions which are positive and monotone increasing, hence ...to certain operator defined on a subset of ∞ (X), that is, the Banach space of all bounded sequences x = { x n } in X with the norm x ... See full document

... In this paper we study the oscillatory and nonoscillatory behavior of the solutions of certain third and fourth order difference equations.. Until recently, excepting the studies by Chen[r] ... See full document

... the oscillatory and asymptotic behavior of solutions of neutral difference equations, see [1]-[5], and the references cited ...the oscillatory and asymptotic behavior of ... See full document

... Asymptotic behavior for non-oscillatory solutions of difference equations with several delays in the neutral term, Journal of Applied Mathematics and Computing, ... See full document

... The article proceeds as follows. In Sect. 2 we show that when 2a |b - c| + a(b + c) < (b - c) 2 , then the equilibrium point of Equation 1 is locally asymptotically stable. In Sect. 3 we prove that the equilibrium ... See full document

... of solutions of certain difference equations analogous to differential equations, the finite order solutions of which do not have wandering ...of solutions with finite order of these ... See full document

... differential equations, the integral transforms were extensively used and thus there are several works on the theory and application of integral transforms such as the Laplace, Fourier, Mellin, and Hankel, to name ... See full document

... of oscillatory solutions for second-order nonlinear neutral delay difference equations are ...non-increasing solutions for corresponding first-order difference inequality, some new estimates for ... See full document

... erence equations are often used in the study of linear and nonlinear physical, physio- logical, and economical problems (for partial review see [3, ...difference equations which someone can find, for ... See full document

... new oscillatory results with respect to the discrete Hermite polynomials of type I, respectively, type II and the Heim-Lorek ...the oscillatory and boundedness properties of the related orthogonality ... See full document