A Computational Numerical Study of Burger Equation with Fractal Fractional Derivative

Sonal Jain, Ho Hon Leung, Firuz Kamalov

Research output: Contribution to journalArticlepeer-review

Abstract

We can observe the idea of fractal medium in a number of real-world problems. In this work, we demonstrate that the idea of the fractal derivative describes the fluid’s movement inside these media in addition to serving as a representation of the fractal sharps. We develop the solution of the viscous Burger equation using various fractal-fractional derivative kernels in this study. We use Newton’s Polynomial approach to solve the fractional Burgers equation in order to solve the numerical procedure. We give simulations for various values of the fractal dimensions to demonstrate the applicability of the current approach in fractal media.

Original languageEnglish
Pages (from-to)99-112
Number of pages14
JournalProgress in Fractional Differentiation and Applications
Volume10
Issue number1
DOIs
Publication statusPublished - 2024

Keywords

  • Adams Bash-forth method
  • fractal-fractional integral operator
  • Newton’s polynomial
  • Viscous Burger equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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