Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation

El-Nabulsi R. A., Khalili Golmankhaneh A.

Communications in Theoretical Physics, vol.73, no.5, 2021 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1088/1572-9494/abeb05
  • Journal Name: Communications in Theoretical Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, INSPEC, zbMATH
  • Keywords: Black-Scholes equation, generalized Burger's equation, fractal calculus, heat kernels, modified diffusion equations
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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.