带有积分边值条件的分数阶微分方程的解
发布时间：2018-11-01 17:16
【摘要】：分数阶微分方程理论是非线性泛函分析领域中一个重要的分支.近几十年来,分数阶微分方程理论得到了越来越多的关注与重视,并逐步发展和完善.分数阶微分是整数阶微分的延伸与拓展,其发展几乎与整数阶微分方程同步,具有广泛的理论意义与实际研究价值,越来越多的科研人员加入到这个领域.本文主要研究了两类带有积分边值条件的分数阶微分方程的解,共分为三章:第一章绪论介绍了有关积分边值问题的背景和发展,并给出分数阶微分方程的相关定义和引理.第二章研究了下面带有积分边值条件的分数阶微分方程多点边值问题在以往研究中,边值条件为积分边值,多点边值其中的一种,本章中将两部分加和,把边值条件变成了 u(i)(1) = ∫01 g(s)u(s)ds+∑jm=1βj u(i)(ηj),并参考[6][7][8][9]的方法,运用Schauder不动点定理与单调迭代方法得到(2.1.1)解的存在性与唯一性.第三章研究了下面带有Riemann-Stieltjes积分边值条件的分数阶微分方程本章在文[11]所研究方程的基础上,将边值条件改为u(1) = ∫01u(s)dA(s),并把原来的二阶导数推广到n阶导数;改变了文[12]方程,并将参数替换成Riemann-Stieltjes积分边值;并参考[12][13][14]的方法,运用不动点指数与Guo-Krasnoselskii不动点定理得到(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，
本文编号：2304577
[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，
本文编号：2304577
本文链接：https://www.wllwen.com/kejilunwen/yysx/2304577.html
