Abstract
This article studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with strip conditions. We extend the idea of four-point nonlocal boundary conditions
(x (0) = sigma x (mu), x (1) = eta x (nu), delta, eta is an element of R, 0 < mu, nu < 1) to nonlocal strip conditions of the form: x(0) = sigma integral(beta)(alpha) x(s)ds, x(1) = eta integral(delta)(gamma) x(s)ds, 0 < alpha < beta < gamma < delta < 1.
These strip conditions may be regarded as six-point boundary conditions. Some new existence and uniqueness results are obtained for this class of nonlocal problems by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed.