This study investigates the interconnections between the traditional Fokker-Planck Equation (FPE) and its fractal counterpart (FFPE), utilizing fractal derivatives. By examining the continuous approximation of fractal derivatives in the FPE, it derives the Plastino-Plastino Equation (PPE), which is commonly associated with Tsallis Statistics. This work deduces the connections between the entropic index and the geometric quantities related to the fractal dimension. Furthermore, it analyzes the implications of these relationships on the dynamics of systems in fractal spaces. In order to assess the effectiveness of both equations, numerical solutions are compared within the context of complex systems dynamics, specifically examining the behaviours of quark-gluon plasma (QGP). The FFPE provides an appropriate description of the dynamics of fractal systems by accounting for the fractal nature of the momentum space, exhibiting distinct behaviours compared to the traditional FPE due to the system's fractal nature. The findings indicate that the fractal equation and its continuous approximation yield similar results in studying dynamics, thereby allowing for interchangeability based on the specific problem at hand.

翻译：本研究利用分形导数探讨了传统福克-普朗克方程（FPE）与其分形对应方程（FFPE）之间的内在联系。通过考察分形导数在FPE中的连续近似，推导出了通常与Tsallis统计相关的普拉斯蒂诺-普拉斯蒂诺方程（PPE）。本文推演了熵指数与分形维数相关几何量之间的关联，并进一步分析了这些关系对分形空间系统动力学的影响。为评估两类方程的有效性，在复杂系统动力学背景下，特别是针对夸克-胶子等离子体（QGP）的行为，比较了其数值解。FFPE通过考虑动量空间的分形性质，恰当描述了分形系统的动力学特征，因系统分形性而表现出与传统FPE迥异的行为。研究结果表明，分形方程及其连续近似在动力学研究中可得出相似结论，因此可根据具体问题在两者间灵活选用。