Existence results for fractional integral boundary value problem involving fractional derivatives on an infinite interval

Abstract

In this paper, we study a integral boundary value problem of fractional differential equation with the nonlinearity depending on fractional derivatives of lower order on an infinite interval. We establish a proper compactness criterion in a special function space. By using the Schauder fixed point theorem and Banach contraction mapping principle, we show the existence and uniqueness results of solutions. Two examples are also provided to illustrate the main results. The results obtained generalize and include some known results.