In this paper, a necessary and sufficient condition, such as the Pontryagin’s maxi-mum principle for a fractional optimal control problem with concentrated parameters, is given by the ordinary fractional differential equation with a coefficient in weighted Lebesgue spaces. We discuss a formulation of fractional optimal control problems by a fractional differential equation in the sense of Caputo fractional derivative. The statement of the fractional optimal control problem is studied by using a new version of the increment method that essentially uses the concept of an adjoint equation of the integral form.

中文翻译：

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加权Lebesgue空间中常微分方程的分数最优控制问题。

本文通过在加权Lebesgue空间中具有系数的普通分数阶微分方程给出了充要参数的分数最优控制问题的必要和充分条件，例如庞特里亚金的极大原理。我们讨论了在Caputo分数导数意义上的分数阶微分方程的分数最优控制问题的表述。分数最优控制问题的陈述是通过使用增量方法的新版本来研究的，增量方法主要使用积分形式的伴随方程的概念。