Anderson, Douglas R.2022-06-132022-06-132017-09-11Anderson, D. R. (2017). Even-order self-adjoint boundary value problems for proportional derivatives. Electronic Journal of Differential Equations, 2017(210), pp. 1-18.1072-6691https://hdl.handle.net/10877/15904In 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.Text18 pages1 file (.pdf)enAttribution 4.0 InternationalProportional derivativesPD controllerGreen's functionSelf-adjoint boundary value problemArticle