Dear researchers
As you know, nowadays, most of the real-world phenomena are modeled by using different fractional operators. Among them, the Caputo and Riemann-Liouville fractional derivatives are the most famous for modeling the processes. Also, in the recent years, two other fractional derivatives called "Caputo-Fabrizio" and "Atangana-Baleanu" are used in many mathematical models. My main question in this regard is:
" What is the physical interpretation of the fractional derivation operators?"
Please see the paper of Igor Podlubny about "geometric and physical Interpretation of fractional integration and fractional differentiation" in the link below.
http://people.tuke.sk/igor.podlubny/pspdf/pifcaa_r.pdf
Hi Dr Sina Etemad . Fractional (fractional-order) derivative is a generalization of integer-order derivative and integral. ... The kernel function of fractional derivative is called memory function, but it does not reflect any physical process. See the link: https://www.nature.com/articles/srep03431
Fractional (fractional-order) derivative is a generalization of integer-order derivative and integral. ... The kernel function of fractional derivative is called memory function9,10, but it does not reflect any physical process.
papers
https://core.ac.uk/download/pdf/82545921.pdf
https://en.wikipedia.org/wiki/Fractional-order_system
https://www2.icp.uni-stuttgart.de/~hilfer/publikationen/pdfo/ZZ-2019-HFCA-47.pdf
Dear Dr. Sina Etemad
This question is very important and many researchers tried to find a simple answer and failed.
From my point of view answer is related to temporal Cantor set that occupies and intermediate position between Euclidean point and line.
If you are trying to average any soft function with Cantor set you can obtain in the limit (when number of columns of the Cantor set N tends to infinity) the desired fractional integral.
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