Solvability Of Boundary Value Problems For Fractional Differential Equations In Banach Spaces

In this paper,by using monotone iterative method of upper and lower solution-s,topological degree theory of condensing mapping,fixed point theorem in abstract space and fixed point index theory of condensing mapping,we discuss the exis-tence,uniqueness and existence of positive solutions for boundary value problems of fractional differential equations in Banach space.where 3<??4,D0+? is the standard Riemann-Liouville fractional derivative.The main results of this paper are as follows:1.By means of maximum principle and monotone iterative method of upper and lower solutions,we obtain the existence and uniqueness of solutions for boundary value problems of fractional differential equations.2.By using the topological degree theory of condensing mapping,Sadovskii's fixed point theorem and new estimation technique of noncompact measure,while f satisfies the first-order growth condition,we obtained the existence of solutions to boundary value problems of fractional differential equations.3.Under the new estimation technique of noncompact measure and order con-dition,based on the fixed point index theory of Condensing Mappings,we obtained the existence of positive solutions for boundary value problems of fractional differ-ential equations in ordered Banach spaces.