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
| Richard I. Avery |
College of Arts and Sciences, Dakota State University
Madison, SD 57042, USA
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