Existence results for boundary value problems of arbitrary order integrodifferential equations in Banach spaces

The study of fractional differential equations has recently gained much attention due to extensive applications of these equations in the mathematical modelling of physical, engineering and biological phenomena. Examples and details concerning the development of the theory, methods and applications of fractional calculus can be found in the books [9], [11] and papers [1], [3], [4], [6], [7]. For some results on boundary value problems of fractional integrodifferential equations, we refer to the papers [2], [5], [12] and the references therein. In this paper, we study the existence and uniqueness of solutions for the following boundary value problem of nonlinear fractional integrodifferential equations (BVP)  Dy(t) = f(t, y(t), (Gy)(t), (Sy)(t)), t ∈ J = [0, T ], y(0) = y0, y ′(0) = y 0 , y ′′(0) = y 0 , · · · , y(n−1)(0) = yn−2 0 , y(n−1)(T ) = yT , (1)