Abstract
We study boundary value problems of nonlinear fractional differential equations and inclusions of order q is an element of (m - 1, m right perpendicular, m >= 2 with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form:
x(1) = Sigma(n-2)(i=1) alpha(i) integral(eta i)(zeta i) x(s)ds,
which can be viewed as an extension of a multi-point nonlocal boundary condition:
x(1) = Sigma(n-2)(i=1) alpha(i)x(eta(i)).
In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments (zeta(i), eta(i)) of the interval [0, 1] and the effect of these strips is accumulated at x = 1. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.