In the literature, fractal derivatives provide many physical insights and geometrical interpretations, but I am wondering where we can apply this particular derivative appropriately. Please refer me to references or examples because I am very interested to learn more about new derivatives and their applications!! I greatly appreciate all the brilliant efforts in this discussion!!
Search "fractal derivative" in Google Scholar and I am sure you will find good resources with just a little effort. RG is mostly oriented for research based discussion, and not for trivial questions the answers of which could be obtained using few strokes of your keyboard.
Hi, you can have a look to the following interesting paper:
Article Fractal calculus and its geometrical explanation
Thank you very much Dr. Richard Epenoy for your answer!! That's a great research paper!!
Flight theory ,Bagley Torvik equation ,fluid mechanic ,burger looks hint equation ,etc
Among the most concrete applications, music: it is possible to build a musical score starting from fractal geometry.
The so-called fractal derivative has been used to deal with non differentiable functions. I never found it could be useful. Therefore, I tried to find an alternative starting from the usual discrete-time fractional derivative, using the concept of "time-scale". See my papers in attach. There are many things to be done, mainly to establish a coherent approach to the continuous-time fractional derivatives, mainly the Grunwald-Letnikov, Liouville and two sided derivatives.
see the following references
Anomalous diffusion modeling by fractal and fractional derivatives
Wen Chen, Hongguang Sun, Xiaodi Zhang, Dean Korošak
https://booksc.xyz/g/Dean%20Koro%C5%A1ak
Thank you very much Dr. Manuel Duarte Ortigueira and Dr. Maged Gumaan Bin-Saad for your answers!! I greatly appreciate them!!
We use it to solve a PDE or an ODE which reprents a model for a problem in many branches of science
In my opinion, whatever be the authorship aspects, integrated (complete in contents) papers are certainly more valuable than differential (fragmented in contents) papers irrespective of disciplines
Transport processes in crowded environments or porous media:
Metzler and Klafter: The random walk's guide to anomalous diffusion: a fractional dynamics approach. Physics Reports 339 (2000) 1-77
There are many references. If needed, I may then mention a few important ones.
Thank you very much, Dr. P. K. Karmakar and Dr. Thomas Neusius for your answes!! I greatly appreciate them!!
P. K. Karmakar I would appreciate that if you could mention only the important references.
Dear Prof.
Because of the good memory and hereditary properties of fractional derivatives, it is often necessary to study the corresponding fractional systems.
There are lot of applications. For example, look for Brachistochrone problem.
From the technological viewpoint, Fractals in Textile Industries, and so forth
The main problem of our concern is still lying on the determination of the fractal dimension in the case of asymmetric atypical irregular patterns
Let us put more efforts to understand more on Fractals and Evolution thereof
Thank you Dr. P. K. Karmakar for all your great answers!!! I greatly appreciate your help!!
In reference with your past request to me, I would like to offer you a few classics for your collective growth in this hot area of Fractals as:
References:
[1] B. B. Mandelbrot, The Fractal Geometry of Nature (W.H. Freeman and Company, New York, 1983).
[2] C. A. Pickover, Chaos and Fractals: A Computer Graphical Journey (Elsevier, New York, 1998).
[3] C. Getz and J. Helmstedt, Graphics with Mathematica Fractals, Julia Sets, Patterns and Natural Forms (Elsevier, London, 2004).
The arena of Fractals is of immense importance in the astrcosmic fluid dynamics
It mostly appears in triggering nonhomologous structure formation processes
The construction of basic formalism is underway
The nature of mysterious Nature is being unfolded in terms of Fractals
Exploring the cosmic universe in a new directional perspective with a strategic application of fractals
Calculating fractal dimension in astroplasmas is of great interest; but, yet to come up
- Badges
- Science topic
- Similar topics
- Mathematics