Fractional-Order and Fractal Dynamic Characteristics of Maritime Decarbonization Pathways Under Alternative Fuel Transition
- 1School of Finance and Trade, Wenzhou Business College, Wenzhou 325035, China
- 2The State Key Laboratory of Green and Low-Carbon Development for Oil-Rich Coal in Western China, Xi’an 710054, China
- 3School of Management, Xi’an University of Science and Technology, Xi’an 710054, China
Abstract
Maritime decarbonization is a complex evolutionary process characterized by nonlinear interactions, delayed responses, path dependence, and multi-scale feedback among economic growth, energy transition, technological innovation, and environmental regulation. Traditional dynamic models based on integer-order assumptions may not fully capture the long-memory effects and anomalous transition behaviors embedded in fleet renewal and alternative fuel diffusion. This study develops a fractal–fractional enhanced 3E (Economic–Energy–Environment) System Dynamics framework to investigate the nonlinear evolution of China’s shipping decarbonization pathways. The proposed model integrates fractional-order dynamic characteristics into the conventional stock–flow representation, allowing historical transition states to influence future fleet evolution through memory-dependent mechanisms. A total cost of ownership (TCO)-based technology selection mechanism is further incorporated to describe the endogenous competition between conventional fuel vessels and alternative-fuel vessels. The framework simultaneously considers trade demand evolution, fleet replacement dynamics, fuel price uncertainty, life-cycle carbon emissions, and carbon-pricing constraints. Historical data from 2013 to 2024 are employed for model calibration, while scenario simulations are conducted from 2025 to 2050 to explore the nonlinear transition characteristics under different technology and policy conditions. The results demonstrate that maritime decarbonization exhibits significant nonlinear and memory-dependent behavior, where the diffusion rate of alternative-fuel vessels is strongly influenced by technological maturity, carbon constraints, and accumulated investment decisions. Compared with conventional dynamic approaches, the fractal–fractional framework provides a more flexible representation of delayed fleet transformation and heterogeneous transition patterns. The findings indicate that deep decarbonization of China’s shipping sector is not only determined by carbon pricing intensity, but also by the interaction between technological progress, economic competitiveness, and long-term system memory. This study provides a novel complex-system perspective for understanding fractal and fractional characteristics in maritime energy transition and offers methodological insights for modeling sustainable transformation pathways in large-scale engineering systems.
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BibTeX
@article{zhang2026fractionalorder,
title = {{Fractional-Order and Fractal Dynamic Characteristics of Maritime Decarbonization Pathways Under Alternative Fuel Transition}},
author = {Tian Zhang and Yihuan Wang and Shaohui Zou},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100696},
url = {https://www.mdpi.com/2504-3110/10/10/696},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Fractional-Order and Fractal Dynamic Characteristics of Maritime Decarbonization Pathways Under Alternative Fuel Transition
AU - Tian Zhang
AU - Yihuan Wang
AU - Shaohui Zou
PY - 2026
DA - 2026/10/03
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100696
UR - https://www.mdpi.com/2504-3110/10/10/696
AB - Maritime decarbonization is a complex evolutionary process characterized by nonlinear interactions, delayed responses, path dependence, and multi-scale feedback among economic growth, energy transition, technological innovation, and environmental regulation. Traditional dynamic models based on integer-order assumptions may not fully capture the long-memory effects and anomalous transition behaviors embedded in fleet renewal and alternative fuel diffusion. This study develops a fractal–fractional enhanced 3E (Economic–Energy–Environment) System Dynamics framework to investigate the nonlinear evolution of China’s shipping decarbonization pathways. The proposed model integrates fractional-order dynamic characteristics into the conventional stock–flow representation, allowing historical transition states to influence future fleet evolution through memory-dependent mechanisms. A total cost of ownership (TCO)-based technology selection mechanism is further incorporated to describe the endogenous competition between conventional fuel vessels and alternative-fuel vessels. The framework simultaneously considers trade demand evolution, fleet replacement dynamics, fuel price uncertainty, life-cycle carbon emissions, and carbon-pricing constraints. Historical data from 2013 to 2024 are employed for model calibration, while scenario simulations are conducted from 2025 to 2050 to explore the nonlinear transition characteristics under different technology and policy conditions. The results demonstrate that maritime decarbonization exhibits significant nonlinear and memory-dependent behavior, where the diffusion rate of alternative-fuel vessels is strongly influenced by technological maturity, carbon constraints, and accumulated investment decisions. Compared with conventional dynamic approaches, the fractal–fractional framework provides a more flexible representation of delayed fleet transformation and heterogeneous transition patterns. The findings indicate that deep decarbonization of China’s shipping sector is not only determined by carbon pricing intensity, but also by the interaction between technological progress, economic competitiveness, and long-term system memory. This study provides a novel complex-system perspective for understanding fractal and fractional characteristics in maritime energy transition and offers methodological insights for modeling sustainable transformation pathways in large-scale engineering systems.
SN - 2504-3110
ER -