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2011•International Journal of Differential EquationsOpen access

Positive Solution to a Fractional Boundary Value Problem

A. Guezane-Lakoud, Rabah Khaldi

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Abstract

A fractional boundary value problem is considered. By means of Banach contraction principle, Leray‐Schauder nonlinear alternative, properties of the Green function, and Guo‐Krasnosel′skii fixed point theorem on cone, some results on the existence, uniqueness, and positivity of solutions are obtained.

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What this paper is about

A fractional boundary value problem is considered. By means of Banach contraction principle, Leray‐Schauder nonlinear alternative, properties of the Green function, and Guo‐Krasnosel′skii fixed point theorem on cone, some results on the existence, uniqueness, and positivity of solutions are obtained.

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Available abstract

A fractional boundary value problem is considered. By means of Banach contraction principle, Leray‐Schauder nonlinear alternative, properties of the Green function, and Guo‐Krasnosel′skii fixed point theorem on cone, some results on the existence, uniqueness, and positivity of solutions are obtained.

Key concepts: Mathematics, Fixed-point theorem, Uniqueness, Contraction principle, Boundary value problem, Mathematical analysis, Cone (formal languages), Contraction mapping

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