Research On Oscillation Of Some Fractional Difference Equations

In recent years,fractional difference equations have gradually become a new topic due to the application in corresponding mathematic model and the approximate cal-culation of fractional differential equations.However,it is extremely difficult to find the exact solutions of fractional difference equations,therefore we turn to study some qualitative properties of these equations,such as the existence,uniqueness,bound-edness,oscillation and asymptotic behavior of solutions of these equations.Indeed,the development of the qualitative properties of fractional difference equations are stil-1 considered to be at its primary stage of progress.As a part of qualitative theory,the oscillation of fractional difference equation have been developed in the past few decades,and there are a series of results.Based on a generalized Riccati transformation and some inequalities,we establish the oscillation criteria for three different kinds of fractional difference equations by using the basic properties of the Riemann-Liouville fractional difference or sum,and integer order difference operator.The thesis is divided into the following five chapters according to the content.Chapter 1 Preference,we introduce the research background of this article and list some basic definitions and lemmas that will be used in this paper.Chapter 2 Motivated by the idea in[6],in this chapter,we are concerned with the oscillation of forced fractional difference equations with damping term of the form:(?),with initial condition ??-1x(t)|t=0=x0.Chapter 3 We study the oscillation of a class of nonlinear fractional difference equations with damping term of the form:(?)Chapter 4 Based on the nonlinear fractional nabla difference system[15],taken the damping term into the above system,we establish the oscillation criteria of 1+?order nabla difference equations of the form:and two examples are provided to demonstrate the usefulness of our results.Chapter 5 Summary,the work done in this paper is summarized and we are looking forward to the next step of research.