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Analysis of solution trajectories of fractional-order systems
Pramana ( IF 2.8 ) Pub Date : 2020-06-29 , DOI: 10.1007/s12043-020-01951-8
Madhuri Patil , Sachin Bhalekar

The behavior of solution trajectories usually changes if we replace the classical derivative in a system with a fractional one. In this article, we throw light on the relation between two trajectories X ( t ) and Y ( t ) of such a system, where the initial point Y (0) is at some point $$X(t_1)$$ X ( t 1 ) of the trajectory X ( t ). In contrast with classical systems, these trajectories X and Y do not follow the same path. Further, we provide a Frenet apparatus for both trajectories in various cases and discuss their effect.

中文翻译:

分数阶系统的解轨迹分析

如果我们用分数阶导数代替系统中的经典导数,解轨迹的行为通常会发生变化。在本文中,我们阐明了这样一个系统的两条轨迹 X ( t ) 和 Y ( t ) 之间的关系,其中初始点 Y (0) 在某个点 $$X(t_1)$$ X ( t 1 ) 的轨迹 X ( t )。与经典系统相比,这些轨迹 X 和 Y 不遵循相同的路径。此外,我们为各种情况下的两种轨迹提供了 Frenet 装置并讨论它们的效果。
更新日期:2020-06-29
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