Diriba, Hailu Daba (2017) Euler- Lagrange Equation for Fractional Variational Problems. Masters thesis, Addis Ababa University.
![[img]](http://thesisbank.jhia.ac.ke/style/images/fileicons/application_pdf.png) |
PDF (Euler- Lagrange Equation for Fractional Variational Problems)
Diriba, Hailu Daba.pdf - Accepted Version Restricted to Repository staff only Download (4MB) | Request a copy |
Abstract
This thesis introduces three new operators and presents some of their properties. It defines a new class of variational problems in terms of these operators and derives Euler-Lagrange equations for this class of problems. It is demonstrated that the left and the right fractional Riemann-Liouville integrals, and the left and the right fractional Riemann-Liouville, Caputo, Riesz-Riemann-Liouville and Riesz-Caputo derivatives are special cases of these operators, and they are obtained by considering a special kernel. Further, the Euler-Lagrange equations developed for functional defined in terms of the left and the right fractional Riemann-Liouville, Caputo, RieszRiemann-Liouville and Riesz-Caputo derivatives are special cases of the EulerLagrange equations developed here. Examples are considered to demonstrate the applications of the new operators and the new Euler-Lagrange equations.
| Item Type: | Thesis (Masters) |
|---|---|
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | Africana |
| Depositing User: | Selom Ghislain |
| Date Deposited: | 27 Jun 2018 13:39 |
| Last Modified: | 27 Jun 2018 13:39 |
| URI: | http://thesisbank.jhia.ac.ke/id/eprint/6019 |
Actions (login required)
 |
View Item |