分数阶一阶导数粒子
Fractional Particle with Fractional First Derivatives
AI总结：
本文提出一种含分数阶一阶导数的经典分数阶粒子模型，推导运动方程与对称性，并解析求解自由粒子和受广义力粒子两个例子。
摘要：
本文提出了一种包含分数阶一阶导数的新型经典分数阶粒子模型。该模型是标准经典粒子的自然推广，其动能是分数阶一阶导数和分数阶线性动量的二次型，类似于经典力学。我们推导了相应的运动方程，并探讨了模型的对称性。此外，我们还给出了用分数阶势能表述的公式。文中解析求解了两个重要例子：自由粒子以及受由分数阶一阶导数表征的广义力作用的粒子。
英文摘要：
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional first derivatives and fractional linear momenta, similarly to classical mechanics. We derive the corresponding equations of motion and explore the symmetries of the model. Also, we present the formulation in terms of fractional potentials. Two important examples are analytically solved: the free particle and the particle subjected to generalized forces characterized by fractional first derivatives.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
