The Existence Of Solutions Of The Boundary Value And Initial Value Problems For Nonlinear Fractional Differential Equations

Fractional diferential equations have gained important applications in eco-nomic,engineering,technology and so on.In recent years,the subject of fractionaldiferential equations has considerable attention from mathematicians.Althoughboundary and initial value problem of integral diferential equations have manyresults,the development progress of boundary and initial value problem of thefractional diferential equations is very slow.In this paper, we main consider the existence of solutions for boundary andinitial value problems of nonlinear fractional diferential equations.The main con-tents as follows:In chapter1,frst we introduce the applied and background of the research.Secondly,introducing main work of the paper.Lastly,introducing some basic proper-ties and concepts of fractional derivative and fractional integral,and fxed pointtheorem.In chapter2,we discuss the existence of solutions for the three points bound-ary value problem with fractional boundary conditions.We frst derive the corre-sponding Green function and discuss its properties.Next,we transform the difer-ential equation into the equivalent integral equation.At this time,we can gainedthe existence results of solutions by using the fxed point theorems.In chapter3,we study the existence of solutions for initial value problems ofnonlinear fractional diferential equations.By using the hybrid fxed point theo-rem,we can obtain the existence of this solution,and extend results in the litera-ture.