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FRACTAL, FRACTIONAL CALCULUS, AND AI: ADVANCED TOOLS DRIVING INNOVATION IN MECHANICAL ENGINEERING
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DOI：10.22190/FUME260218004H.png)
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Abstract
En 中文
In addressing the macro-micro nonlinear challenges encountered in mechanical engineering, this article employs a multifaceted approach by integrating non-self-similar fractal theory, fractal-based fractional calculus and fractal-fractional AI. It thereby proposes novel concepts, including scale-dependent two-scale fractal derivatives and fractal-embedded Caputo calculus, which have not been previously documented. The validation of the framework is achieved through the use of a fractal MEMS photoacoustic transducer case, which derives fractal-modified stiffness and pull-in voltage models to balance device stability and efficiency. The work elucidates the three-step integration logic of the three tools, analyses their engineering applications, and outlines future directions in multi-scale modelling, lightweight AI, digital twin integration and standardization. This provides new theoretical and technical support for intelligent mechanical engineering innovation.
Keywords:
Non-self-similar fractal theory
Fractal-based fractional calculus
Fractal-fractional artificial intelligence
Mechanical engineering
Cross-scale modeling
Nonlinear dynamics
Journal
F
IF:
11.8
Papers:
301
Citations:
1.6K
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Cited Papers