Even-order self-adjoint boundary value problems for proportional derivatives
| dc.contributor.author | Anderson, Douglas R. | |
| dc.date.accessioned | 2022-06-13T12:36:34Z | |
| dc.date.available | 2022-06-13T12:36:34Z | |
| dc.date.issued | 2017-09-11 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 18 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15904 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Proportional derivatives | |
| dc.subject | PD controller | |
| dc.subject | Green's function | |
| dc.subject | Self-adjoint boundary value problem | |
| dc.title | Even-order self-adjoint boundary value problems for proportional derivatives | |
| dc.type | Article |