Research On The BVPs Of Fractional Differential Equations With Hilfer Derivatives

The problem of fractional differential equations is a subject which have been studied by many scholars in recent years,especially the study of the initial value problems and boundary value problems for nonlinear fractional differential equations.Many new results have been achieved.Due to the wide application,the discussion of related issues still requires us to do in-depth research.This paper discuss the initial value problems and boundary value problems of fractional differential equations with Hilfer derivatives.In the second chapter,we study the properties of the two-parameter Mittag-Leffler function in the solution of the boundary value problem.We use the Banach comtraction mapping principle to prove the existence and uniqueness of the solution.Next,this paper uses the Krasnosel’skii fixed point theorem,the upper and lower solution theorem and the Schauder fixed point theorem to discuss the existence of positive solutions under the condition of < 0.Finally,some examples are given to illustrate our main results.In the third chapter,we consider a initial value problems for fractional order differential inclusion with Hilfer derivative in Banach spaces.We obtain an existence result of solutions for inclusion problems by using Bohnenblust-Karlins flxed point theorem.Finally,some examples are given to illustrate our main results.