Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition

Christina A.  Hollon; Jeffrey T.  Neugebauer

doi:10.3934/proc.2015.0615

Article Contents

2015, Volume 2015: 615-620. Doi: 10.3934/proc.2015.0615 open access

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Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition

Christina A. Hollon^1, and
Jeffrey T. Neugebauer^1,

1.
Department of Mathematics and Statistics, Eastern Kentucky University, Richmond, Kentucky 40475

Received: August 31, 2014

Revised: April 30, 2015

Published: October 2015

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Abstract

In this paper, we apply Krasnosel'skii's cone expansion and compression fixed point theorem to show the existence of at least one positive solution to the nonlinear fractional boundary value problem $D^\alpha_{0^+} u + a(t)f(u)=0$, $0 < t < 1$, $1 < \alpha \le 2$, satisfying boundary conditions $u(0)=D^\beta_{0^+} u(1)=0$, $0\le\beta\le1$.

Keywords:

Fractional derivative,
positive solution.

Mathematics Subject Classification: Primary: 34B18, 26A33; Secondary: 34B15.

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References

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