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Fractal Calculus and Homotopy for Nonlinear Equations on Curves
Journal article   Peer reviewed

Fractal Calculus and Homotopy for Nonlinear Equations on Curves

Alireza Khalili Golmankhaneh, Rawid Banchuin, Palle E. T. Jørgensen and Donal O’Regan
International journal of applied and computational mathematics, Vol.12(4), 56
06/17/2026
DOI: 10.1007/s40819-026-02124-8

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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.
Mathematics Applications of Mathematics Computational Science and Engineering Mathematical and Computational Physics Mathematical Modeling and Industrial Mathematics Mathematics and Statistics Nuclear Energy Operations Research/Decision Theory Original Paper Theoretical

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