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The Research of Some Problems on Fraction Differential Equations

Author: LiuGaiYun
Tutor: OuYangZiGen
School: Nanhua University
Course: Applied Mathematics
Keywords: Fractional Differential Equations Existence Uniqueness Lerey_Schauder fixed point theory Green's function
CLC: O175.8
Type: Master's thesis
Year: 2011
Downloads: 79
Quote: 0
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Abstract


In recent years, fractional differential and integral equations in engineering, technology, economics , ecology and other fields have a wide range of applications, so fractional differential and integral equations study aroused the attention of scholars , especially the existence and uniqueness research . This paper is organized as follows : The first chapter, we introduce the development of fractional differential equations , research content , meaning and Fractional Differential Equations of development history. Chapter II study a class of fractional differential equations with infinite delay existence of solutions , we use the contraction mapping principle and fixed point theorem on the existence and uniqueness of solutions of equations theory . Chapter III , a class of fractional differential equations Boundary Value Problems. We used to construct the Green's function solution of the problem , in order to find multiple positive solutions for this problem . Finally , we summarize the conclusions and made some research prospects for future research .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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