Positive Solutions And Numerical Solutions Of Fractional Differential Equations

Fractional calculus has a long history.From the beginning of its establishment to the middle of twenty century,more than two hundreds years,the studies were concentrated on a pure theoretical field.Later,with the development of the application of fractional calculus,such as the description of memory and hereditary properties of various materials,increasingly used to model problems in rheology and in materials and mechanical systems,signal processing and systems identification,control and robotics, and other areas of applications,the research on fractional differential equations(FDEs) became more and more popular.Especially in recent years,theory and applications of fractional differential equations are developing intensively.This paper mainly discusses the existence of positive solutions of FDEs and their numerical solutions.In the investigation of FDEs,the existence of positive solutions is of importance.On the other hand,very few references have been found to deal with fractional differential equations by wavelets.Thus,it’s an useful attempt to solve FDEs by wavelets.This thesis consists of four chapters,which can be divided into two parts.The first part(Chapters2,Chapters3) focuses on the theoretical analysis for the existence of positive solutions of nonlinear fractional differential equations and nonlinear fractional functional equations.The second part(Chapters4) concentrates on numerical computation for FDEs by means of wavelets.