Publication
Analysis and numerical approximation of tempered fractional calculus of variations problems
| Summary: | In this paper, we study variational problems where the cost functional involves the tempered Caputo fractional derivative. Several important optimization conditions are derived to find the optimal solution. Sufficient and necessary conditions are presented for different variational problems. For example, the cases of integral (isoperimetric problem) and holonomic constraints are considered, as well as problems with high order derivatives. A numerical scheme is proposed to determine approximations of the solution and it is illustrated through some examples |
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| Main Authors: | Almeida, Ricardo |
| Other Authors: | Morgado, M. Luísa |
| Subject: | Euler–Lagrange equation Numerical methods Tempered fractional derivative |
| Year: | 2019 |
| Country: | Portugal |
| Document type: | article |
| Access type: | restricted access |
| Associated institution: | Universidade de Aveiro |
| Language: | English |
| Origin: | RIA - Repositório Institucional da Universidade de Aveiro |
| Summary: | In this paper, we study variational problems where the cost functional involves the tempered Caputo fractional derivative. Several important optimization conditions are derived to find the optimal solution. Sufficient and necessary conditions are presented for different variational problems. For example, the cases of integral (isoperimetric problem) and holonomic constraints are considered, as well as problems with high order derivatives. A numerical scheme is proposed to determine approximations of the solution and it is illustrated through some examples |
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