Journal article
Fractal Green Function Theory
Communications in nonlinear science & numerical simulation, Vol.152(Part E), 109402
01/2026
DOI: 10.1016/j.cnsns.2025.109402
Abstract
This paper provides a comprehensive study of fractal calculus and its application to differential equations within fractal spaces. It begins with a review of fractal calculus, covering fundamental definitions and measures related to fractal sets. The necessary preliminaries for understanding fractal Green’s functions are introduced, laying the groundwork for further exploration. We develop the fractal Green’s function for inhomogeneous fractal differential equations and extend this to the fractal Helmholtz equation. The application of the fractal Green’s function to the Schrödinger equation is also investigated, focusing on the fractal Schrödinger-type differential equation with a fractal mesonic potential. Additionally, the scattering amplitude is derived within the fractal Born approximation, offering insights into scattering phenomena in fractal spaces. The findings highlight the significant impact of fractal geometry on classical and quantum mechanics and present new methods for addressing problems in fractal environments.
Details
- Title: Subtitle
- Fractal Green Function Theory
- Creators
- Alireza Khalili GolmankhanehCarlo CattaniHemanta KalitaShigeru FuruichiPalle E.T. Jørgensen
- Resource Type
- Journal article
- Publication Details
- Communications in nonlinear science & numerical simulation, Vol.152(Part E), 109402
- DOI
- 10.1016/j.cnsns.2025.109402
- ISSN
- 1007-5704
- eISSN
- 1878-7274
- Publisher
- ELSEVIER
- Language
- English
- Electronic publication date
- 10/10/2025
- Date published
- 01/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985016012202771
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