M. Rybaczuk et al., The concept of physical and fractal dimension II. The differential calculus in dimensional spaces, CHAOS SOL F, 12(13), 2001, pp. 2537-2552
The projective dimensional analysis based on the projective extension of sc
aling group and projective dimensional function is studied. The differentia
l calculus corresponding to geometry of dimensional spaces is constructed a
nd examined. At the next step we explore the projective extension of dimens
ional derivatives. Simple fractal models of various processes with changing
fractal dimension illustrate the proposed methods. (C) 2001 Elsevier Scien
ce Ltd. All rights reserved.