Existence and uniqueness of solutions for nonlinear fractional differential equations with non-separated type integral boundary conditions

In this paper, we study a boundary value problem of nonlinear fractional differential equations of order q (1< q ≤ 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.