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Some Problems of Fractional Differential Equations

Author: WangLin
Tutor: OuYangZiGen
School: Nanhua University
Course: Applied Mathematics
Keywords: Fractional differential equation Fixed-point theorem Positive solutions Boundary value problem Green function
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 132
Quote: 0
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Abstract


Study of Some Problems For The Fractional Differential Equations with the increasing development of science and technology, differential equations are powerful instrument to analyze and solve problems in the modem science and technology .It plays an important role in the field of economic and financial insurance, the analysis of the structure of the number of biological species ,and the control and prevention of diseases of insect and so on. It become an extremely active research direction.It is very important research for the existence results of solutions of fractional order differential equation . In recent years , many authors have investigated fractional differential equations because that it is applied in many fields extensively such as physics , mechanics and engineering etc. Many authors have obtained the existence conditions for fractional differential equations [1-5]. In particular the boundary value problem of non-linear fractional order differential equations is one of most active domains of functional analysis at present. And the existence results of positive solutions for boundary value problem of nonlinear fractional differential equations is also the hot spot which has been discussed in recent years . So , it has become a very important domain of differential equation research at present.In this paper, we studied the following problems:They are the existence results of the solutions of fractional order differential equation, and the existence results of positive solutions for boundary value problem of nonlinear fractional order differential equations.We divided this paper into four chapters:In chapter one , it is a brief introduction of the history and present situation of the study about the fractional different equation, and purpose of studied.In chapter two, the contraction mapping principle and the Banach fixed point theorem are used to investigate the existence of solutions for fractional order neutral functional differential equations with infinite delay. In chapter three, A class of the both operators of fractional order differentiation be investigated in a Banach space in this paper,based on the contraction mapping principle and Leray-Schauder fixed point theorem,it obtain some sufficient conditions for the existence of the solutions. Example is inserted to illustrate this results.In chapter four, we studied the existence of positive solutions for boundary value problem of nonlinear fractional differential equation on the base of the property of Green function. We also use Krassnosekii’s fixed point theorem to obtain the main results.

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