分数阶微分方程与差分方程的振动性研究
发布时间：2018-10-25 11:17
【摘要】：作为动力学的基础,微分方程的定性性质受到越来越多的关注,近年来,分数阶微分方程的研究成为热点.分数阶微分方程定性性质的研究也产生了一系列成果,其中,分数阶微分方程与差分方程的振动性研究引起了一些专家的重视,其结果也具有广泛的应用.本文在借鉴前人研究方法的基础上,利用广义的Riccati变换和一些不等式,研究分数阶微分方程、分数阶差分方程、时标动态方程的振动性准则.根据内容本文分为以下四章:第一章绪论,主要介绍本文用到的关于分数阶微分方程、分数阶差分方程、时标动态方程的基本定义性质以及引理.第二章利用修正Riemann-Liouville分数阶导数的性质,研究一类新的含修正Riemann-Liouville分数阶导数的方程的振动性准则.(?)其中DαX(t)是x(t)的α ∈ (0,1)阶修正Riemann-Liouville分数阶导数.第三章在文献[26, 28]的启发下,研究(?)的振动性.第四章在文献[1, 29]的启发下,研究(?)的振动性.
[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 伪 X (t) is a modified Riemann-Liouville fractional derivative of order 伪 鈭，
本文编号：2293548
[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 伪 X (t) is a modified Riemann-Liouville fractional derivative of order 伪 鈭，
本文编号：2293548
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