【摘要】：分數(shù)階微分方程理論是非線性泛函分析領域中一個重要的分支.近幾十年來,分數(shù)階微分方程理論得到了越來越多的關注與重視,并逐步發(fā)展和完善.分數(shù)階微分是整數(shù)階微分的延伸與拓展,其發(fā)展幾乎與整數(shù)階微分方程同步,具有廣泛的理論意義與實際研究價值,越來越多的科研人員加入到這個領域.本文主要研究了兩類帶有積分邊值條件的分數(shù)階微分方程的解,共分為三章:第一章緒論介紹了有關積分邊值問題的背景和發(fā)展,并給出分數(shù)階微分方程的相關定義和引理.第二章研究了下面帶有積分邊值條件的分數(shù)階微分方程多點邊值問題在以往研究中,邊值條件為積分邊值,多點邊值其中的一種,本章中將兩部分加和,把邊值條件變成了 u(i)(1) = ∫01 g(s)u(s)ds+∑jm=1βj u(i)(ηj),并參考[6][7][8][9]的方法,運用Schauder不動點定理與單調迭代方法得到(2.1.1)解的存在性與唯一性.第三章研究了下面帶有Riemann-Stieltjes積分邊值條件的分數(shù)階微分方程本章在文[11]所研究方程的基礎上,將邊值條件改為u(1) = ∫01u(s)dA(s),并把原來的二階導數(shù)推廣到n階導數(shù);改變了文[12]方程,并將參數(shù)替換成Riemann-Stieltjes積分邊值;并參考[12][13][14]的方法,運用不動點指數(shù)與Guo-Krasnoselskii不動點定理得到(3.1.1)解的存在性.
[Abstract]:Fractional differential equation theory is an important branch of nonlinear functional analysis. In recent decades, the theory of fractional differential equations has been paid more and more attention, and gradually developed and improved. Fractional differential is an extension and extension of integer-order differential, and its development is almost synchronous with integer-order differential equation. It has extensive theoretical significance and practical research value. More and more researchers join in this field. In this paper, we mainly study the solutions of two kinds of fractional differential equations with integral boundary value conditions, which are divided into three chapters: the first chapter introduces the background and development of integral boundary value problems, and gives the relevant definitions and Lemma of fractional differential equations. In the second chapter, we study the following multipoint boundary value problems of fractional differential equations with integral boundary value conditions. In previous studies, the boundary value conditions are integral boundary values, one of which is multipoint boundary values. In this chapter, two parts are added together. The boundary value condition is changed to u (i) (1) = 01 g (s) u (s) ds 鈭，

本文編號：2304577