Journal article
Fractal Calculus and Homotopy for Nonlinear Equations on Curves
International journal of applied and computational mathematics, Vol.12(4), 56
06/17/2026
DOI: 10.1007/s40819-026-02124-8
Abstract
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.
Details
- Title: Subtitle
- Fractal Calculus and Homotopy for Nonlinear Equations on Curves
- Creators
- Alireza Khalili Golmankhaneh - Islamic Azad University of UrmiaRawid Banchuin - Siam UniversityPalle E. T. Jørgensen - Department of Mathematics, The University of IowaDonal O’Regan - Ollscoil na Gaillimhe – University of Galway
- Resource Type
- Journal article
- Publication Details
- International journal of applied and computational mathematics, Vol.12(4), 56
- DOI
- 10.1007/s40819-026-02124-8
- ISSN
- 2349-5103
- eISSN
- 2199-5796
- Publisher
- Springer India
- Language
- English
- Date published
- 06/17/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985175360202771
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