Electron. J. Differential Equations,
Vol. 2017 (2017), No. 210, pp. 118.
Evenorder selfadjoint boundary value problems for proportional derivatives
Douglas R. Anderson
Abstract:
In this study, even order selfadjoint differential equations incorporating
recently introduced proportional derivatives, and their associated
selfadjoint boundary conditions, are discussed. Using quasi derivatives,
a Lagrange bracket and bilinear functional are used to obtain a Lagrange
identity and Green's formula; this also leads to the classification of
selfadjoint boundary conditions. Next we connect the selfadjoint
differential equations with the theory of Hamiltonian systems and
(n,n)disconjugacy. Specific formulas of Green's functions for two
and four iterated proportional derivatives are also derived.
Submitted July 7, 2017. Published September 11, 2017.
Math Subject Classifications: 26A24, 34A05, 49J15, 49K15.
Key Words: Proportional derivatives; PD controller; Green's function;
selfadjoint boundary value problem.
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Douglas R. Anderson
Department of Mathematics
Concordia College
Moorhead, MN 56562, USA
email: andersod@cord.edu

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