Combined Fractional Variational Problems of Variable Order and Some Computational Aspects
| Autor: | Tavares, Dina, Almeida, Ricardo, Torres, Delfim F. M. |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | J. Comput. Appl. Math. 339 (2018), 374--388 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.cam.2017.04.042 |
| Popis: | We study two generalizations of fractional variational problems by considering higher-order derivatives and a state time delay. We prove a higher-order integration by parts formula involving a Caputo fractional derivative of variable order and we establish several necessary optimality conditions for functionals containing a combined Caputo derivative of variable fractional order. Because the endpoint is considered to be free, we also deduce associated transversality conditions. In the end, we consider functionals with a time delay and deduce corresponding optimality conditions. Some examples are given to illustrate the new results. Computational aspects are discussed using the open source software package Chebfun. Comment: This is a preprint of a paper whose final and definite form is with 'Journal of Computational and Applied Mathematics', ISSN: 0377-0427. Submitted 15-Feb-2017; Revised 17-Apr-2017; Accepted 21-Apr-2017 |
| Databáze: | arXiv |
| Externí odkaz: |
|