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Open Access Research

Positive solutions of a fractional thermostat model

Juan J Nieto12* and Johnatan Pimentel1

Author Affiliations

1 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain

2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

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Boundary Value Problems 2013, 2013:5  doi:10.1186/1687-2770-2013-5

Published: 16 January 2013

Abstract

We study the existence of positive solutions of a nonlinear fractional heat equation with nonlocal boundary conditions depending on a positive parameter. Our results extend the second-order thermostat model to the non-integer case. We base our analysis on the known Guo-Krasnosel’skii fixed point theorem on cones.