Douglas R. Anderson, Richard I. Avery
Abstract:
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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