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<p>In this paper, we apply the Homotopy Analysis Method (HAM) to fractal ordinary and partial differential equations defined on fractal curves. After briefly reviewing the essential tools of fractal calculus, we adapt the HAM framework to the fractal setting and show how the convergence–control parameter improves the accuracy of the homotopy series. Several illustrative examples of nonlinear fractal ODEs and PDEs are solved, demonstrating the efficiency and flexibility of the method for analytic approximation on fractal geometries.</p>

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Fractal Calculus and Homotopy for Nonlinear Equations on Curves

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Alireza Golmankhaneh Khalili,
  • Rawid Banchuin,
  • Palle E. T. Jørgensen,
  • Donal O’Regan

摘要

In this paper, we apply the Homotopy Analysis Method (HAM) to fractal ordinary and partial differential equations defined on fractal curves. After briefly reviewing the essential tools of fractal calculus, we adapt the HAM framework to the fractal setting and show how the convergence–control parameter improves the accuracy of the homotopy series. Several illustrative examples of nonlinear fractal ODEs and PDEs are solved, demonstrating the efficiency and flexibility of the method for analytic approximation on fractal geometries.