标题： 可 conformable 缩放与临界动力学：相变的统一框架 显示英文标题

标题： Conformable Scaling and Critical Dynamics: A Unified Framework for Phase Transitions

摘要： 我们研究了可 conformable 导数在连续相变附近建模临界现象的应用。 通过将一个变形参数引入微分结构，我们推导出热力学可观测量（如比热、磁化率、磁化强度和相干长度）的统一表达式，每个量在临界温度附近均表现出幂律行为。 conformable 导数框架自然地将尺度不变性和临界迟滞效应嵌入动力学中，而无需采用完全非局部的分数阶微积分。 构建了修正的 Ginzburg-Landau 方程来模拟超导转变，得出序参量和伦敦穿透深度的解析表达式。 铌的实验数据验证了该模型的适用性，显示出良好的拟合效果，并捕捉到了 Tc 附近的不对称标度行为。 这项工作在经典平均场理论与广义标度框架之间架起了一座桥梁，对理论建模和实验分析均有意义。 显示英文摘要

摘要： We investigate the application of conformable derivatives to model critical phenomena near continuous phase transitions. By incorporating a deformation parameter into the differential structure, we derive unified expressions for thermodynamic observables such as heat capacity, magnetization, susceptibility, and coherence length, each exhibiting power-law behavior near the critical temperature. The conformable derivative framework naturally embeds scale invariance and critical slowing down into the dynamics without resorting to fully nonlocal fractional calculus. Modified Ginzburg-Landau equations are constructed to model superconducting transitions, leading to analytical expressions for the order parameter and London penetration depth. Experimental data from niobium confirm the model's applicability, showing excellent fits and capturing asymmetric scaling behavior around Tc. This work offers a bridge between classical mean-field theory and generalized scaling frameworks, with implications for both theoretical modeling and experimental analysis.