Journal
ENTROPY
Volume 20, Issue 7, Pages -Publisher
MDPI
DOI: 10.3390/e20070504
Keywords
Hausdorff dimension; middle- Cantor sets; staircase function; C-calculus; diffusion on fractal; random walk
Categories
Funding
- Engineering and Physical Sciences Research Council, UK
Ask authors/readers for more resources
In this paper, we study C-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the C-calculus on the generalized Cantor sets known as middle- Cantor sets. We have suggested a calculus on the middle- Cantor sets for different values of with 0<<1. Differential equations on the middle- Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available