Existence of solutions for boundary value problems of fractional differential equation in Banach spaces

摘要

In this paper, with the help of a new estimation technique for the measure of noncompactness, under more general conditions of growth and noncompactness measure, combining with the Sadovskii's fixed point theorem and Leray-Schauder type fixed point theorem of condensing mapping, we obtain the existence of solutions for the following boundary value problems of fractional differential equation in Banach spaces where 1 < β ≤ 2 is a real number, J = [0, 1],~CD_(0+)~β is the Caputo fractional derivative of order β, f : J × E → E is continuous, E is a Banach spaces, θ is the zero element of E.