AN ORDERING ON GREEN’S FUNCTIONS FOR A FAMILY OF TWO-POINT BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

PAUL ELOE; JEFFREY W. LYONS; JEFFREY T. NEUGEBAUER

Title	AN ORDERING ON GREEN’S FUNCTIONS FOR A FAMILY OF TWO-POINT BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS
Publication Type	Journal Article
Year of Publication	2015
Authors	ELOE, PAUL, LYONS, JEFFREYW, NEUGEBAUER, JEFFREYT
Volume	19
Issue	3
Start Page	453
Pagination	9
Date Published	2015
ISSN	1083-2564
AMS	26A33, 34A08, 34A40
Abstract	Let ${ 2 ≤ n }$ denote an integer and let ${ n−1 < α ≤ n.}$ For each ${0 < b, 0 ≤ β ≤ n−1 }$, the authors will construct the Green’s function,${ G(b, β;t, s),}$ of the two-point boundary value problem for the fractional differential equation $${ D^α_{0+}u + h(t) = 0, \ \ \ 0 < t < b, }$$ $${ u^{(i)} (0) = 0, \ \ \ i = 0, . . . n − 2, \ \ \ D^β_{0+}u(b) = 0,}$$ where ${ D^α_{0+} }$ and ${ D^β_{0+} }$ denote the standard Riemann-Liouville derivatives. The authors will compare Green’s functions, ${ G(b1, β;t, s) }$ and ${ G(b2, β;t, s) }$ or ${ G(b, β1;t, s)}$ and ${ G(b, β2;t, s),}$ and the authors will show the existence of a unique limiting function as ${ b → ∞.}$ An application to a nonlinear problem will be given.
URL	http://www.acadsol.eu/en/articles/19/3/10.pdf
Refereed Designation	Refereed
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