Even-order self-adjoint boundary value problems for proportional derivatives
Date
2017-09-11
Authors
Anderson, Douglas R.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Proportional derivatives, PD controller, Green's function, Self-adjoint boundary value problem
Citation
Anderson, D. R. (2017). Even-order self-adjoint boundary value problems for proportional derivatives. Electronic Journal of Differential Equations, 2017(210), pp. 1-18.
Rights
Attribution 4.0 International