Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

摘要: Abstract One way to deal with physical problems on nowhere differentiable fractals is the mapping of these into corresponding for continuum a proper fractal metric. On this different definitions metric were suggested account essential features. In work we develop differential vector calculus in three-dimensional non-Euclidean The forms and Laplacian are introduced, fundamental identities operators established integral theorems proved by employing version quaternionic analysis Moisil–Teodoresco operator, which has been introduced partially developed paper. relations between conventional revealed. It should be emphasized that provides comprehensive mathematical formalism any suitable definition This offers novel tool study physics fractals.