In this study, we prove that modified diffusion equations, including the generalized Burgers’ equation with variable coefficients, can be derived from the Black-Scholes equation with a time-dependent parameter based on the propagator method known in quantum and statistical physics. The extension for the case of a local fractal derivative is also addressed and analyzed.

中文翻译：

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具有可变系数的广义热扩散方程及其来自 Black-Scholes 方程的分形

在这项研究中，我们证明了修正的扩散方程，包括具有可变系数的广义 Burgers 方程，可以从具有时间相关参数的 Black-Scholes 方程导出，该方程基于量子和统计物理学中已知的传播器方法。还讨论和分析了局部分形导数情况的扩展。