We conduct a thorough exploration of the magnetic flows and physical dynamics exhibited by point charged particles in three-dimensional ordinary space. Our methodology is grounded in the application of conformable methods. Initially, we refine the general treatment to derive velocity and acceleration vector fields for point particles traversing conformable curves under the influence of distinct force fields. Subsequently, our inquiry extends into the realm of magnetism, where we investigate various types of dynamical magnetic curves that emerge from characterizing the movement of charged particles along conformable curves. In addition to this, we introduce the Fermi–Walker conformable derivative and provide an alternative representation for a unit-speed conformable curve by leveraging the Fermi–Walker connection. Throughout the entirety of the paper, we establish a meaningful correlation between the consistent motion of conformable charged particles and the trajectories dictated by specific external forces within the \(\alpha \)-Frenet–Serret frame. The application of fractional calculus plays a pivotal role in our investigations, a facet we meticulously delve into in the paper. This work significantly contributes to an enhanced comprehension of magnetic phenomena and dynamics, offering valuable insights into the behavior of charged particles within conformable frameworks.

我们对三维普通空间中点带电粒子表现出的磁流和物理动力学进行了彻底的探索。我们的方法论基于一致方法的应用。最初，我们改进了一般处理方法，以导出在不同力场的影响下穿过一致曲线的点粒子的速度和加速度矢量场。随后，我们的研究扩展到磁性领域，我们研究了通过表征带电粒子沿着顺应曲线的运动而出现的各种类型的动态磁曲线。除此之外，我们还引入了费米-沃克适形导数，并利用费米-沃克连接为单位速度适形曲线提供了另一种表示形式。在整篇论文中，我们在一致带电粒子的一致运动与\(\alpha \) -Frenet-Serret 框架内由特定外力决定的轨迹之间建立了有意义的相关性。分数阶微积分的应用在我们的研究中发挥着关键作用，我们在论文中仔细研究了这一方面。这项工作极大地有助于增强对磁现象和动力学的理解，为一致框架内带电粒子的行为提供了有价值的见解。