In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:0+ is the standard Riemann-Liouville differentiation, and f : [0, 1] × [0, ∞) → [0, ∞) is continuous. By means of some fixed-point theorems on cone, some existence and multiplicity results of positive solutions are obtained. The proofs are based upon the reduction of problem considered to the equivalent Fredholm integral equation of second kind.  2005 Elsevier Inc. All rights reserved.

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In this article, we consider the following boundary value problem of nonlinear fractional differential equation with p-Laplacian operator:continuous. One of the difficulties here is that the corresponding Green's function G(t, s) is singular at s = 0. By the use of an approximation method and fixed point theorems on cone, some existence and multiplicity results of positive solutions are acquired. Some examples are presented to illustrate the main results.

In this paper, the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order are obtained. Our results are based on some fixed point theorems. Some examples are also presented to illustrate the main results. MSC: 34B15; 34A08