Department of Mathematics
Concordia College
Moorhead, MN 56562, USA
email: andersod@cord.edu
Douglas R. Anderson
Abstract:
In this study, even order self-adjoint differential equations incorporating
recently introduced proportional derivatives, and their associated
self-adjoint 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
self-adjoint boundary conditions. Next we connect the self-adjoint
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;
self-adjoint 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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