Electron. J. Diff. Equ., Vol. 2015 (2015), No. 29, pp. 1-10.

Fractional-order boundary value problem with Sturm-Liouville boundary conditions

Douglas R. Anderson, Richard I. Avery

Using the new conformable fractional derivative, which differs from the Riemann-Liouville and Caputo fractional derivatives, we reformulate the second-order conjugate boundary value problem in this new setting. Utilizing the corresponding positive fractional Green's function, we apply a functional compression-expansion fixed point theorem to prove the existence of a positive solution. We then compare our results favorably to those based on the Riemann-Liouville fractional derivative.

Submitted October 25, 2014. Published January 29, 2015.
Math Subject Classifications: 26A33.
Key Words: Conformable fractional derivative; boundary value problem; positivity; Green's function; conjugate conditions.

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Douglas R. Anderson
Department of Mathematics, Concordia College
Moorhead, MN 56562, USA
email: andersod@cord.edu
Richard I. Avery
College of Arts and Sciences, Dakota State University
Madison, SD 57042, USA
email: rich.avery@dsu.edu

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