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

Zhang, Xinguang; Liu, Lishan; Wu, Yong Hong; Wiwatanapataphee, Benchawan

doi:10.1016/j.amc.2014.12.068

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Authors

Zhang, Xinguang

Liu, Lishan

Wu, Yong Hong

Wiwatanapataphee, Benchawan

Date

2015

Type

Journal Article

Metadata

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Citation

Zhang, X. and Liu, L. and Wu, Y.H. and Wiwatanapataphee, B. 2015. The spectral analysis for a singular fractional differential equation with a signed measure. Applied Mathematics & Computation. 257: pp. 252-263.

Source Title

Applied Mathematics & Computation

DOI

10.1016/j.amc.2014.12.068

ISSN

0096-3003

School

Department of Mathematics and Statistics

URI

http://hdl.handle.net/20.500.11937/46987

Collection

Curtin Research Publications

Abstract

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.