本文選題：分?jǐn)?shù)階微積分　切入點(diǎn)：退化系統(tǒng)　出處：《安徽大學(xué)》2017年碩士論文

【摘要】：隨著現(xiàn)代社會科技和工業(yè)的快速發(fā)展和需求,不斷提高數(shù)學(xué)模型的精確度和真實(shí)性成為最為重要的課題之一。事實(shí)上,大多實(shí)際系統(tǒng)的動態(tài)過程本質(zhì)上是分?jǐn)?shù)階的,比如:電磁波傳導(dǎo)系統(tǒng)、粘彈性系統(tǒng)、流體力學(xué)系統(tǒng)、生物系統(tǒng)等。對于這些系統(tǒng)而言,要想對其進(jìn)行更準(zhǔn)確地分析和綜合,就必須用分?jǐn)?shù)階微分系統(tǒng)來描述。與此同時,人們也發(fā)現(xiàn)時滯和退化也是實(shí)際系統(tǒng)的普遍現(xiàn)象。因此,研究含有時滯和退化的分?jǐn)?shù)階微分系統(tǒng)具有重要的理論價(jià)值和現(xiàn)實(shí)意義。全文共分為五章。第一章為緒論,對本文的研究背景進(jìn)行了簡要的介紹。第二章為預(yù)備知識,本章主要介紹了分?jǐn)?shù)階微積分的基本概念和退化系統(tǒng)理論的基礎(chǔ)知識,并且給出了本文所需的常用引理。第三章討論了分?jǐn)?shù)階阻尼系統(tǒng)的解的存在唯一性,給出了分?jǐn)?shù)階阻尼系統(tǒng)解的存在唯一的充分條件。第四章討論了分?jǐn)?shù)階退化時滯系統(tǒng)的有限時間穩(wěn)定性,給出了分?jǐn)?shù)階退化時滯微分系統(tǒng)的有限時間穩(wěn)定的充分條件。第五章討論了分?jǐn)?shù)階退化系統(tǒng)的可容許性,給出了階數(shù)為1到2的分?jǐn)?shù)階退化系統(tǒng)可容許的充分條件。
[Abstract]:With the rapid development and demand of science, technology and industry in modern society, increasing the accuracy and authenticity of mathematical models has become one of the most important topics. For example, electromagnetic wave conduction systems, viscoelastic systems, hydrodynamic systems, biological systems, etc. For these systems to be more accurately analyzed and synthesized, they must be described by fractional differential systems. It is also found that delay and degeneracy are common phenomena in practical systems. Therefore, it is of great theoretical value and practical significance to study fractional differential systems with delay and degenerate. The paper is divided into five chapters. In the second chapter, the basic concepts of fractional calculus and the basic knowledge of degenerate system theory are introduced. In chapter 3, we discuss the existence and uniqueness of the solution of the fractional damping system. Sufficient conditions for the existence and uniqueness of solutions for fractional damped systems are given. In chapter 4, the finite time stability of fractional degenerate time-delay systems is discussed. The sufficient conditions for finite time stability of fractional degenerate delay differential systems are given. In chapter 5, the admissibility of fractional degenerate systems is discussed, and the sufficient conditions for the admissibility of fractional degenerate systems of order 1 to 2 are given.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：1653636