Journal article
Cauchy problem approach to biharmonic models in fractal time and space
Chaos, solitons and fractals, Vol.205, 117772
04/2026
DOI: 10.1016/j.chaos.2025.117772
Abstract
This paper pioneers the application of fractal calculus to higher α-order differential models defined on non-Euclidean spaces. We establish and solve the fractal Cauchy problem for the biharmonic equation, providing detailed visualizations that demonstrate the unique influence of fractal geometry on solution behavior. The methodology is subsequently validated through applications to critical physical scenarios, namely the cooling of a clamped thin beam and the vibration of a thin elastic plate. These case studies reveal how the fractal dimensions of time and space fundamentally modify the dynamics of classical systems. Overall, this study underscores the effectiveness and necessity of fractal calculus for accurately capturing complex, scale-dependent phenomena in non-standard frameworks.
•A fractal Cauchy problem for the biharmonic equation is developed.•Solutions are obtained in fractal time–space.•Applications to thin beam cooling and plate vibration.
Details
- Title: Subtitle
- Cauchy problem approach to biharmonic models in fractal time and space
- Creators
- Alireza Khalili Golmankhaneh - Islamic Azad University of UrmiaDonatella Bongiorno - University of PalermoPalle E.T. Jørgensen - Department of Mathematics, The University of Iowa, Iowa City, 52242-1419, IA, USA
- Resource Type
- Journal article
- Publication Details
- Chaos, solitons and fractals, Vol.205, 117772
- DOI
- 10.1016/j.chaos.2025.117772
- ISSN
- 0960-0779
- eISSN
- 1873-2887
- Publisher
- Elsevier Ltd
- Language
- English
- Date published
- 04/2026
- Academic Unit
- Mathematics
- Record Identifier
- 9985113257102771
Metrics
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