Document Type
Article
Publication Date
11-22-2016
Publication Source
Electronic Journal of Differential Equations
Abstract
We consider families of two-point boundary value problems for fractional differential equations where the fractional derivative is assumed to be the Riemann-Liouville 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.
Inclusive pages
1-13
ISBN/ISSN
1072-6691
Document Version
Published Version
Copyright
Copyright © 2016, Texas State University.
Publisher
Texas State University
Volume
2016
Peer Reviewed
yes
eCommons Citation
Eloe, Paul W. and Neugebauer, Jeffrey T., "Convolutions and Green’s Functions for Two Families of Boundary Value Problems for Fractional Differential Equations" (2016). Mathematics Faculty Publications. 75.
https://ecommons.udayton.edu/mth_fac_pub/75
COinS
Comments
This document has been made available for download in accordance with the publisher's policy on self-archiving.
Permission documentation on file.