Boundary Value Problems For Several Kinds Of Fractional Differential Equations

With the enrichment of the theory of boundary value problem of fractional differential equation and its application in more and more fields,the boundary value problem of fractional differential equation has become an important subject studied and explored by many scholars,which makes the study of boundary value problems developed.In recent years,with the development of science and technology,fractional calculus theory not only has important applications in the fields of civil engineering,mechanical engineering,thermal energy system,fluid mechanics,viscoelasticity and image processing but also indispensable in the fields of control theory,biology,finance and other natural and social sciences.The boundary conditions of the model are changed and improved on the basis of the study of the literature.We can establish new models.The existence and uniqueness of the solution of the model are studied by using the method of upper and lower solutions and several fixed point theorems.There are five chapters in this thesis.The first chapter introduces the research background,research content and preliminary knowledge.The main content is from Chapter 2 to chapter 4.In the second chapter,by constructing the Green function and using Banach contraction fixed point theorem,we can obtain the existence interval of the solution of the boundary value problem of the fractional differential equation of Caputo type.In chapter 3,by using fixed point theorem,we obtain the existence interval of boundary value problems of Caputo type and Riemann-Liouville type for fractional differential equations,in particular,we estimate the length of the interval;in chapter 4,we obtain existence and uniqueness of the solution for Hadamard fractional differential equation with integral boundary conditions by using fixed point theorem and upper and lower solution methods.In the last chapter,we summarize the full text.