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<p>This research delves into analyzing the invariant properties and conservation laws (CLs) governing the (3+1)-dimensional (3D) time-fractional Bateman–Burgers (BB) equation, employing the Riemann Liouville (RL) fractional derivative. The fractional Lie symmetry method is employed to ascertain the symmetry attributes of this equation. Consequently, the equation is transformed into a fractional ordinary differential equation (FODE) using the Erdélyi–Kober (EK) fractional differential operator. Additionally, the paper derives new conserved vectors for the 3D time-fractional BB equation using the formal Lagrangian and a detailed derivation based on the new conservation theorem. The explicit solutions and their stability are also examined and analyzed.</p>

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Lie group analysis and conservation laws for the time-fractional 3D Bateman–Burgers equation

  • 期刊论文

  • 发表日期：

    2025年4月7日

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  • Nida Zinat,
  • Akhtar Hussain,
  • A. H. Kara,
  • F. D. Zaman

摘要

This research delves into analyzing the invariant properties and conservation laws (CLs) governing the (3+1)-dimensional (3D) time-fractional Bateman–Burgers (BB) equation, employing the Riemann Liouville (RL) fractional derivative. The fractional Lie symmetry method is employed to ascertain the symmetry attributes of this equation. Consequently, the equation is transformed into a fractional ordinary differential equation (FODE) using the Erdélyi–Kober (EK) fractional differential operator. Additionally, the paper derives new conserved vectors for the 3D time-fractional BB equation using the formal Lagrangian and a detailed derivation based on the new conservation theorem. The explicit solutions and their stability are also examined and analyzed.