Research On Several Kinnds Of Existence Of Solutions For Fractional Differential Equations

Fractional calculus is the study of the number of arbitrary order calculus theory.It isthe expansion and extension of the integer order calculus.There is an important practicalsignificance in mathematical model.With the development of science andtechnology,fractional calculus theory has important applications in physics,chemistry,biology and other natural sciences, and also has a very important role in thecontrol theory, finance and other social sciences.It has a very high research value andpractical value.Therefore, the existence of solutions for fractional differential equationshas the very important significance and research value.Based on the theory of fractional differential equations,the paper studies the multiplepoint boundary value problem of fractional differential equation finite domain,the mixedboundary value problem of fractional differential equations and the multiple fractionaldifferential equation boundary value problem.The existence of the solutions for the aboveproblem and the examples are given.Firstly, the paper studies the infinite domain of higher order differential equations offractional order.It carries on the thorough discussion according to the research of loworder multiple point boundary value problems uses the equivalence relation betweenoperator fixed point and the solution of the equation and uses the Schauder fixed pointtheorem and the method of iteration,gets the sufficient condition of the existence ofsolutions of boundary value problems.Secondly, the essay discusses the higher-order fractional differential equations ofmixed type boundary value problem by using the Guo-Krasnosel ’skii fixed point,foundsthe fixed point on cone,proves the existence of solution for boundary value problems.Finally, using the Schauder fixed point theorem researched the fractional differentialequations of higher order boundary value problems.