Researched On Oscillation Behavior Of Fractional Differential And Difference Equations

As the basis of dynamics, the qualitative properties of differential equations have attracted more and more attention. The research on fractional differential equations become hot topic. The research on the qualitative properties of fractional differential equations have produced a series of conclusions. Some authors take attention on the oscillation of the fractional differential and difference equations, and their results have a wide range of application.In this paper, by using generalized Riccati transformation and some inequalities, os-cillation behavior of fractional differential equations, fractional difference equations and dynamic equation on time scales will be studied.This paper includes the following four parts:Chapter 1 Preference, we mainly introduced some basic definitions and properties about fractional differential, fractional derivative, dynamic equations on time scales, and lemmas.Chapter 2 Based on the properties of modified Riemann-Liouville fractional deriva-tive, the oscillatory of solutions to fractional differential equations with a damping term will be presented:(?)where D_?x is the modified Riemann-Liouville fractional derivative of order ?? (0,1),Chapter 3 Motivated by [26, 28], we will research the oscillation criteria for the following fractional differential equations with damping term (?)Chapter 4 Motivated by [1, 29], we will research the oscillation behavior of the following generalized Emden-Fowler dynamic equations:(?)...