【摘要】：作為動力學(xué)的基礎(chǔ),微分方程的定性性質(zhì)受到越來越多的關(guān)注,近年來,分數(shù)階微分方程的研究成為熱點.分數(shù)階微分方程定性性質(zhì)的研究也產(chǎn)生了一系列成果,其中,分數(shù)階微分方程與差分方程的振動性研究引起了一些專家的重視,其結(jié)果也具有廣泛的應(yīng)用.本文在借鑒前人研究方法的基礎(chǔ)上,利用廣義的Riccati變換和一些不等式,研究分數(shù)階微分方程、分數(shù)階差分方程、時標動態(tài)方程的振動性準則.根據(jù)內(nèi)容本文分為以下四章:第一章緒論,主要介紹本文用到的關(guān)于分數(shù)階微分方程、分數(shù)階差分方程、時標動態(tài)方程的基本定義性質(zhì)以及引理.第二章利用修正Riemann-Liouville分數(shù)階導(dǎo)數(shù)的性質(zhì),研究一類新的含修正Riemann-Liouville分數(shù)階導(dǎo)數(shù)的方程的振動性準則.(?)其中DαX(t)是x(t)的α ∈ (0,1)階修正Riemann-Liouville分數(shù)階導(dǎo)數(shù).第三章在文獻[26, 28]的啟發(fā)下,研究(?)的振動性.第四章在文獻[1, 29]的啟發(fā)下,研究(?)的振動性.
[Abstract]:As the basis of dynamics, the qualitative properties of differential equations have attracted more and more attention. In recent years, the research of fractional differential equations has become a hot topic. The study of qualitative properties of fractional differential equations has also produced a series of results, among which, the oscillation of fractional differential equations and difference equations has attracted the attention of some experts, and the results are also widely used. In this paper, the oscillatory criteria of fractional differential equation, fractional difference equation and time scale dynamic equation are studied by using generalized Riccati transform and some inequalities based on the previous research methods. This paper is divided into four chapters according to the content: the first chapter is an introduction, mainly introduces the fractional differential equation, fractional difference equation, time scale dynamic equation basic definition properties and Lemma used in this paper. In chapter 2, by using the properties of modified Riemann-Liouville fractional derivative, we study the oscillatory criteria for a class of equations with modified Riemann-Liouville fractional derivative. Where D 偽 X (t) is a modified Riemann-Liouville fractional derivative of order 偽 鈭，

本文編號：2293548