Electron. J. Differential Equations,
Vol. 2016 (2016), No. 297, pp. 113.
Convolutions and Green's functions for two families of
boundary value problems for fractional differential equations
Paul W. Eloe, Jeffrey T. Neugebauer
Abstract:
We consider families of twopoint boundary value problems for fractional
differential equations where the fractional derivative is assumed to
be the RiemannLiouville fractional derivative. The problems considered
are such that appropriate differential operators commute and the problems
can be constructed as nested boundary value problems for lower order
fractional differential equations. Green's functions are then constructed
as convolutions of lower order Green's functions. Comparison theorems are
known for the Green's functions for the lower order problems and so, we
obtain analogous comparison theorems for the two families of higher order
equations considered here. We also pose a related open question for a
family of Green's functions that do not apparently have convolution
representations.
Submitted August 31, 2016 Published November 22, 2016.
Math Subject Classifications: 26A33, 34A08, 34A40, 26D20.
Key Words: Fractional boundary value problem; fractional differential inequalities.
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Paul W. Eloe
Department of Mathematics
University of Dayton
Dayton, Ohio 45469, USA
email: peloe1@udayton.edu


Jeffrey T. Neugebauer
Department of Mathematics and Statistics
Eastern Kentucky University
Richmond, Kentucky 40475, USA
email: Jeffrey.Neugebauer@eku.edu

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