FRACTAL, FRACTIONAL CALCULUS, AND AI: ADVANCED TOOLS DRIVING INNOVATION IN MECHANICAL ENGINEERING

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.