The fractional variational problem of Herglotz type for the case where the Lagrangian depends on generalized fractional derivatives, the free endpoints conditions, and a real parameter is studied. This type of problem generalizes several problems recently studied in the literature. Moreover, it allows us to unify conservative and non-conservative dynamical processes in the same model. The dependence of the Lagrangian with respect to the boundaries and a free parameter is effective and transforms the standard Herglotz’s variational problem into a problem of a different nature.

中文翻译：

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Herglotz 的分数变分原理用于一类新的依赖于边界和实参数的问题

研究了拉格朗日函数依赖于广义分数阶导数、自由端点条件和实参数的情况下的 Herglotz 型分数变分问题。这种类型的问题概括了最近在文献中研究的几个问题。此外，它允许我们在同一模型中统一保守和非保守的动力学过程。拉格朗日对边界和自由参数的依赖是有效的，并将标准 Herglotz 变分问题转换为不同性质的问题。