The spectral analysis for a singular fractional differential equation with a signed measure

In this paper, by using the spectral analysis of the relevant linear operator and Gelfand's formula, we obtain some properties of the first eigenvalue of a fractional differential equation. Based on these properties, the fixed point index of the nonlinear operator is calculated explicitly and some sufficient conditions for the existence of positive solutions are established. (C) 2014 Elsevier Inc. All rights reserved.