تقرير
Fractal derivatives, fractional derivatives and $q$-deformed calculus
| العنوان: | Fractal derivatives, fractional derivatives and $q$-deformed calculus |
|---|---|
| المؤلفون: | Deppman, Airton, Megias, Eugenio, Pasechnik, Roman |
| المصدر: | Entropy 2023, 25(7), 1008 |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics High Energy Physics - Phenomenology Mathematical Physics Nonlinear Sciences Physics (Other) |
| مصطلحات موضوعية: | Mathematical Physics, High Energy Physics - Phenomenology, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Physics - Applied Physics, Physics - Plasma Physics |
| الوصف: | This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The paper distinguishes between the derivative of a function on a fractal domain and the derivative of a fractal function, where the image is a fractal space. Different continuous approximations for the fractal derivative are discussed, and it is shown that the $q$-calculus derivative is a continuous approximation of the fractal derivative of a fractal function. A similar version can be obtained for the derivative of a function on a fractal space. Caputo's derivative is also proportional to a continuous approximation of the fractal derivative, and the corresponding approximation of the derivative of a fractional function leads to a Caputo-like derivative. This work has implications for studies of fractional differential equations, anomalous diffusion, information and epidemic spread in fractal systems, and fractal geometry. Comment: 7 pages, 1 figure; v2 extended Discussion and Conclusions section, added Fig. 1 and references. Typos corrected. It matches the version published in MDPI Entropy |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3390/e25071008 |
| URL الوصول: | http://arxiv.org/abs/2305.04633 |
| رقم الأكسشن: | edsarx.2305.04633 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.3390/e25071008 |
|---|