Existence results for nonlocal boundary value problems of fractional differential equations and inclusions with strip conditions

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) = σx (μ), x (1) = ηx (v), σ, η ∈ ℝ, 0 < μ, v < 1) to nonlocal strip conditions of the form: (Equation presented) 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. © 2012 Ahmad and Ntouyas; licensee Springer.