DIFFUSION ON FRACTAL OBJECTS MODELING AND ITS PHYSICS-INFORMED NEURAL NETWORK SOLUTION

Abstract

Fractional operators are the main tools to describe diffusion problems on fractal objects. This paper first shows the equivalence between conformable fractional derivative and fractal derivative, and then investigates various models for the diffusion on fractal objects by the conformable fractional derivative and its generalized form. The recommended models are solved by the mesh-free physics-informed neural network method with high computational effectiveness and universality.