A generalization of a fractional variational problem with dependence on the boundaries and a real parameter
In this paper, we present a new fractional variational problem where the Lagrangian depends not only on the independent variable, an unknown function and its left- and right-sided Caputo fractional derivatives with respect to another function, but also on the endpoint conditions and a free parameter...
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| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2021
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| Texto completo: | http://hdl.handle.net/10773/30987 |
| País: | Portugal |
| Oai: | oai:ria.ua.pt:10773/30987 |
| Resumo: | In this paper, we present a new fractional variational problem where the Lagrangian depends not only on the independent variable, an unknown function and its left- and right-sided Caputo fractional derivatives with respect to another function, but also on the endpoint conditions and a free parameter. The main results of this paper are necessary and sufficient optimality conditions for variational problems with or without isoperimetric and holonomic restrictions. Our results not only provide a generalization to previous results but also give new contributions in fractional variational calculus. Finally, we present some examples to illustrate our results. |
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