Abstract
In this paper, we discuss a new class of nonlocal boundary value problems of fractional differential equations and inclusions with a new integral boundary condition. This new boundary condition states that the value of the unknown function at an arbitrary (local) point xi is proportional to the contribution due to a sub-strip of arbitrary length (1 - eta) that is, x(xi) = a integral(1)(eta) x(s)ds, where 0 < xi < 1 and a is constant of proportionality. The existence of solutions for the given problems is shown by means of contraction mapping principle, a fixed point theorem due to O'Regan and nonlinear alternative for multivalued maps. The results are well illustrated with the aid of examples.