A short note about fractional calculus, mainly because of a Sri Lankan in the forefront. That is Udita Katugampola who got his Bachelors from Colombo University in 2002. He has created the Katugampola fractional operators that are integral operators that generalize the Riemann–Liouville and the Hadamard fractional operators into a unique form.
Why fractional operators matter. Conventional calculus has its limits when we try to model complex situations. Allows to understand and model the finest details of physical processes with unprecedented precision. Patient response in anaesthesia is one. Helps solve all manner of problems, from detecting cancer to preventing the spread of pollution to making more efficient batteries. Recent (2015) developments in Image processing, edge detection, image restoration and fractional differentiation as a tool to reveal faint objects in
astronomical images.
(I can see the potential for Satellite Image processing and wish had this tool when I did Satellite Image processing).
The briefest possible introduction to fractional operators.
(note: Most of it is well beyond my comprehension and pay grade.)
For those who remember their classical calculus, derivatives or integrals are done by integers. eg d2y/dx2 is the second derivative.
A fractional derivative would be d(1/2)y/dx(1/2)
The easiest to understand is the fractional derivatives of exponential functions.
That about the limit of my understanding. The above and more is explained in A Child's Garden of Fractional Derivatives.
Some Links
https://www.newscientist.com/article/mg25233603-200-how-an-upgrade-on-calculus-is-taking-maths-into-uncharted-territory
https://www.researchgate.net/publication/239745037_A_Child%27s_Garden_of_Fractional_Derivatives
https://arxiv.org/abs/0910.2381
Udita Katugampola's website, fractional differentiation links page
https://sites.google.com/site/uditanalin/fraccalc
"Conventional calculus has its limits when we try to model complex situations. Allows to understand and model the finest details of physical processes with unprecedented precision. Patient response in anaesthesia is one"--lifted word for word from a different source. Surfing the web and collating information is one thing, smartly understanding the information is another. You fail at the latter and excel at the former.
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