Fractional Derivatives, Part 1 - Powers
Vložit
- čas přidán 5. 08. 2024
- How do you define the half-derivative of a function? Does this even make sense?! As it turns out it's not too difficult to do this once you understand the gamma function. We start with some basic examples of integer-order derivatives of powers of x and then generalize this to fractional-order derivatives. All of the background for this is covered in a previous video on the gamma function, linked below.
The Gamma Function: • The Gamma Function
Looking for a specific problem or topic? Try checking my website:
www.blacktshirtmathprofessor....
► Artist Attribution
Music By: "After The Fall"
Track Name: "Pieces"
Music Published by: Chill Out Records LLC
License: Creative Commons Attribution 4.0 International (CC BY - 4.0)
Full license here: creativecommons.org/licenses
As always, a wonderful video. Fractional derivatives are a fascinating concept that I hadn't thought of before. It was also enormously helpful to link it with the gamma function, which I only learned about yesterday.
outstanding sir ....hats off
Great explanation!
Please, include more videos on fractional calculus. If possible, create a complete course on this important and interesting area. Presently, we don't find any systematic series of lectures on the subject to be understood by a beginner. Hope to hear from you soon.
It’s on my list! I have a series planned out that involves an approach using Taylor/Maclaurin series and the Caputo fractional derivative. I just need to find a balance now that all of my courses are back in person.
شرح رائع . متقن ومبسط . بارك الله فيكم
Asombroso!
Interesting. I wonder what real applicaions are on the horizon with fractional derivatives.
Fantastic!!
Nice video, very informative.
Thanks, fellow mathematician!
Professor, your explanation is amazing, but I can't find the second lecture on fractional derivatives... I need this lecture💔
I've been really curious about this, but it makes a lot of sense! Is there a way to generalize it for all f(x) ∈ R as oppose to all x^n ∈ R? I'm loving these videos, they get better every time!
There’s actually two ways to generalize this! One approach uses Taylor/Maclaurin series representations (which involve powers) and the other is the Caputo fractional derivative. I’m still planning these videos since even the simplest elementary functions require using special functions to find their fractional derivatives.
If you’re curious right now theres a post on my Instagram page where I calculate the Caputo half derivative of the exponential function. It involves the error function.
Hey prof - going to be watching this and the prerequisite videos you linked. You should toss them into a playlist! I also really like the idea of doing little mini-courses on interesting subjects like this. I think it's a great idea to differentiate yourself (pun intended) from the crowd. I think covering topics like complex numbers and their calculus, and maybe even some variational calculus in the future would be really cool, though one step at a time of course! Good luck.
I definitely will. For fractional derivatives I’m basically forced into introducing special functions so that will probably be my first mini course: gamma function, Bessel functions, orthogonal polynomials.
I’ll make a promise right now: mini courses on basics of complex analysis and variational calculus will be my plans for June.
@@BlackTshirtMathProfessor Wow, thank you professor. I'm definitely looking forward to that.
@@BlackTshirtMathProfessor Haha, did we achieve liftoff? Was it a Reddit post? Congrats, of course.
It was a combination of dozens of Reddit posts, posting in the Lofi Girl/Chilled Cow chat, and a few targeted ads in specific countries. It’s a grind but it’s paying off 💪🏻
Cool video!
yeah ;))
Congratulations for your explanation
Thanks, fellow mathematician!
wow.....thank you
How we find half derivative of sinx, cosx, lnx , and sinh,sin-1(x) etc
I watched both Gamma function video and this one. Both has valuable information. But I have to say that it doesnt work for me. I need to find out how Gamma(1/3) and so on come out. Im searching numerical approximation you mention in the video. If you could pls help me about that i will be appreciate it. Thanks a lot.
I believe that there is no known exact form for the value of Gamma(1/3).
thanks
You’re welcome, fellow mathematician!
@@BlackTshirtMathProfessor please keep make another video, I love your contents
I’m planning on it. It’s a bit harder to find time to record with life stuff and all of my courses going back to in-person.
Sir ,Plz let me know a proper book for learning fractional derivatives .
I don’t know of a full book on fractional calculus but the Wikipedia page on fractional calculus has a lot of references.
I am doing research in fractional calculus, if there is anybody doing work on same topic please let me know, i need ur help
Check out the Caputo fractional derivative, if you’re not already familiar with it
I know, i wand to do work with expert person in fractional calculus
What is half derivative of Gamma(x) function ?
looks a lot like the binomial formula
Good observation!