Fractional Derivatives, Part 1 - Powers

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.

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► 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)

[johnivan]

Great work dear Black T-shirt proffesor.

[waqarahmed]

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.

[manardjaber]

شرح رائع . متقن ومبسط . بارك الله فيكم

[MohdAbuolwan]

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.

[masashibata]

Interesting. I wonder what real applicaions are on the horizon with fractional derivatives.

[Krispio]

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.

[hdhdhdhd-wk]

Professor, your explanation is amazing, but I can't find the second lecture on fractional derivatives... I need this lecture💔

[georgeklimov]

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!

[mudasirhussainveesar]

How we find half derivative of sinx, cosx, lnx, and sinh, sin-1(x) etc

[dr.rahulgupta]

Sir, Plz let me know a proper book for learning fractional derivatives .

[cloudyforever]

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.

[mariusziwaniuk]

What is half derivative of Gamma(x) function ?

[PauloConstantino]

but when you integrate the fractional derivative of X, you get the wrong result. So you need fractional integrals as well

[muhammadkhalid]

I am doing research in fractional calculus, if there is anybody doing work on same topic please let me know, i need ur help