The Fractional Derivative, what is it? | Introduction to Fractional Calculus

[@vcubingx]

Support me on Patreon! patreon.com/vcubingx There are a lot of minor mistakes, like I said indefinite instead of definite and z instead of n. Sorry about that. Enjoy the video anyway :)

[@bennettgardiner8936]

Also at 7min you have an extra 'f', otherwise a really nice introduction, well done mate.

[@vcubingx]

@@bennettgardiner8936 you're right, thanks

[@stephenv796]

@@vcubingx Would you consider doing a video on Fractional Brownian motion please, superb video btw :)

[@vcubingx]

@@stephenv796 Thanks! I'll look into it and see if it's worth a video

[@pmz558]

@@vcubingx a video on fbm would be awesome

[@blackpenredpen]

This is an awesome video! I enjoyed it very much!

[@vcubingx]

Thank you so much Steve! I really appreciate it 😊

[@emonph4463]

@blackpenredpen i love u🥺

[@alonsojoaquin8845]

@@emonph4463 x2

[@Santi._.403]

This was awesome!! I’m about to graduate in pure math as an undergrad and have been playing around with the Gamma Function! I feel like I just got a new toy!!!

[@aaronsmith6632]

I started figuring out fractional calculus on my own during my Math minor. It's cool to finally learn about it officially.

[@francoiswessels8062]

😂

[@zeeshanchaudhry3324]

I'd like some extra info on the Gamma Fxn. Curious about its limitations. I love how concise you were in this video and the transition in n from a set of positive integers to n as the set of all positive real numbers to n as the set of all numbers. Your mistakes are forgivable since this is so well-presented on a conceptual level. Thank you so much for this work.

[@physicslover1950]

That was awesome the animation of the Tautochrone Problem that you showed very Brilliantly describes why time period of Simple harmonic motion is independent of the displacement from the mean position . Like the time period of a simple pendulums is independent of the amplitude of vibration. The animation that you showed at tge end of the video reveals a mystery of transformation of a function into its derivatives or its integrals. Very very awesome visualizations. 💚💚💚 Even if I have studied calculus 3 but it still seems like I am a kindergarten student staring hopelessly at a teacher who is teaching university level students and I can't catch him even if I try my best. One question of mine is that can we move the integral sign inside a square root . If we want to to this then can it be accomplished with the help of fractional integral?

[@iamstickfigure]

11:00 This is saying that the semi-derivative of the constant function f(x)=1 with respect to x is 1/sqrt(pi*x) ? If I'm understanding that correctly, that is very odd indeed. Since the derivative of any constant is 0, which is another constant. So the transition between a full derivative and f(x) has some weird non-constant states in-between. I would love to see the animation of D^a(1) where a animates between 0 and 1

[@Perplaxus]

When the function x is being transformed by the Differintegral operator, at 9:16, it seems to me that the square root of x appears for a brief moment, at 9:17. Is the square root of x the Differintegral of x to some value between 0 and 1? Update: Yeah now I saw the rest of the video. The answer is Almost.

[@anilsharma-ev2my]

See how fractional number are added by formula for adding first n natural numbers also adding fractional values as well ???

[@all462]

3blue1brown will be proud of you. Edit: 3blue1brown is proud of you. 😊

[@joulev]

Pedro Dumper What do you mean?

[@dylana.2011]

Pedro Dumper explaining math concepts with minimalist animations is definitely not copyrightable lmao. And thank god its not, that would be an absolutely trash idea. I’m sure 3blue1brown would be really happy that this guy is competently explaining difficult concepts in a concise video

[@dylana.2011]

@Pedro Dumper ah I see what you mean. In my opinion that's different from saying a video is literally copyright infringement. Fair point though. Hell, if I made this video I'd take it as a huge compliment if someone said that it was that similar to 3b1b lol. He's basically the epitome of KZbin math vids these days

[@joulev]

@Pedro Dumper Look, the animation is from an open-source Python library called manim github.com/3b1b/manim. 3Blue1Brown wrote that and *everyone is allowed to use that*! This is not copyrighted or anything - this is completely legal. Research before making false accusations.

[@riuza9681]

@@joulev Yes this is what I thought too. 3b1b does not own this software-like animation thing. I think the goal of 3b1b is clearly to popularize "the right way to think about maths" and moreover how to vizualise it to have an intuition. Just imagine if everyone get inspiration from 3b1b and it would become the common way to do maths, how far even humanity could get into complexity easily. I think 3b1b would be very happy of this and even do tutorials on how to use computers for this (maybe he did already i didn't check) Sorry for my english not my first language.

[@bon12121]

YES WE WANT THE VIDEO ON THE GAMMA FUNCTION. I'M GOING TO SEARCH YOUR PLAYLISTS NOW FINGERS CROSSED.

[@rosgori]

It seems that everything is beautiful with Manim

[@lehpares]

You’re explaining higher calculus and you are a person: no one would make fun of you. Fantastic video, by the way.

[@vcubingx]

Thank you so much!!!

[@poonamdeshpande7832]

@@vcubingx indeed you have done a great job as i did read lot of material on FD and wanted to explain easily in my paper now i am able to understand it and able to put in my words. thanks

[@satwikchivukula8905]

@@poonamdeshpande7832 can you please suggest me any book that'll be great to learn this FDE topic that I can find online.

[@poonamdeshpande7832]

@@satwikchivukula8905 all I have is research papers as the FD textbooks are very expensive but there is one group on FB which provides freePDFs form there I downloaded one ebook on FD

[@satwikchivukula8905]

@@poonamdeshpande7832 name of that page???

[@dragon-xt4vw]

Oh dear god. I almost don't wanna know. Almost.

[@brockbaldridge7620]

dragon21516 lol me too

[@gt3293]

I want to know, but I can't understand this yet... Just missing too many pieces right now

[@thegoodkidboy7726]

Dwarf Fortress kills the cheap computer.

[@rafee_adnan]

"I'M SORRY I CAN'T PRONOUNCE ANYTHING MB PLES DONT MAKE FUN OF ME THX".. we won't :)

[@vcubingx]

Ahahahahaha

[@jevinliu4658]

We should make fun of him saying that...

[@anujbangad3973]

@engineer99 I did the same to look what just happened..

[@connorhorman]

> The Gamma Function is not defined for n < 0 Actually, It isn’t defined for Re(z) in Negative integers. It is well defined for all complex numbers with negative real components, as long as that component is not an integer.

[@vcubingx]

you're right it is defined; my fault for the mistake

[@racheline_nya]

i mean, the graph clearly shows it. also, since Γ(n)=(n-1)!, we can see that it should be undefined for negative integers and 0, because the factorial of a negative integer contains division by 0, which is illegal.

[@epicmorphism2240]

It is defined for them, but not for the ones with Im(z) = 0. So for example -1+i is defined, whereas -1 or -2 isn't. You easily can evaluate -1 + i with the recursiv definition of the gamma function Gamma(z) = Gamm(z+1)/z.

[@tonaxysam]

@@epicmorphism2240 so do you want to take imagonary diferencition?

[@F_A_F123]

It's well defined for all complex numbers with non-zero imaginary part, no matter what the real part is. So Γ(x) has points of where it is undefined, not lines

[@benjamimapancake6429]

I thought that this was 3B1B until I heard the voice. Loved the video, loved the content, learned something! Good video.

[@benjamimapancake6429]

A lot of this is over my head, though.

[@vcubingx]

Yep thats one of the things I realized after making the video: if you don't give your full attention, its hard to understand everything. I think I'm gonna go a bit slower next time, but thanks anyway!!

[@benjamimapancake6429]

I think that it's just over my head, I'm going into Calc this year.

[@vcubingx]

@@benjamimapancake6429 ah, now it makes sense

[@nicholassimon-brecke733]

Found this video from Showmakers interview of 3b1b. You have earned yourself another sub because of your quality content and to support the growth of manim. Cheers!! :-)

[@vcubingx]

Thank you! Was I mentioned in the interview or something? I'm just curious as to how exactly you found my content

[@Shamisen100]

There are some applications of fractional calculus in the design of PID-like controllers, but using fractional integral and fractional derivative instead of the simple integral and derivative used in PID. In some cases, those show some advantages in terms of robustness. A good survey about this topic is Dastjerdi, Ali Ahmadi, et al. "Linear fractional order controllers; A survey in the frequency domain." Annual Reviews in Control (2019).

[@hellodarknessmyoldfriend2976]

Bro wrf ur literally the first guy I’ve seen to cover such complex topics like fractional calculus with beautiful animations. Subbed immediately keep it up vro and plz don’t worry bout ppl making fun of u, literally No One is thinking that: ) 👍👍

[@modolief]

Ummm ... 3Blue1Brown ? You've _got_ to check out those videos. kzbin.info/door/YO_jab_esuFRV4b17AJtAw

[@flyingdonkey5488]

Yea it's quite similar to 3blue1brown

[@AdityakrishnaMr]

Thus video immediately reminded me of 3B1B!

[@hlessirah7148]

@@flyingdonkey5488 he uses the same software (manim) to make the animation It's an open source library made by 3b1b

[@jaikumar848]

Sometimes I love KZbin recommendation

[@tatoute1]

We can simply define fractional derivative using Fourier transformation. As the Fourrier transformation of a n-derived function is scaled by the n-power of the frequency, we can replace n by a real value and use inverse Fourrier to get the result. BTW this explain the oscillation that occurs at 9:23.

[@razterizer]

Yep. The Gibbs phenomenon.

[@eugeneimbangyorteza]

That's exactly what I've thought the moment I read the title.

[@Lucky10279]

Interesting.

[@angeldude101]

I was wondering if the Fourier transform would show up since the transition to the derivative in the animation showed some wave-like distortion around x=0 that I recognized as being reminiscent of what happens when taking the Fourier transform of a function with sharp jumps.

[@abdulazizmemesh2791]

I'd love to see a video about the gamma function + Pi function I really like your channel, keep up the good work I have two suggestion: 1- mention how advanced the math is before starting the video, and what I need to know to understand the content 2- Just watching a video is not going to be sufficient for understanding a concept, I hope that you put a link in the description for practice questions whether a pdf file or another video or a website

[@vcubingx]

Good points! I'll definitely be sure to include that in my next videos. Thanks for watching and thanks for the feedback 😊

[@GabrielPohl]

What? I thought it was a recent idea, but Leibniz already thought of it!

[@johnopalko5223]

Leibniz and Euler, between the two of them, have thought of _everything._ 😁

[@Vindignatio]

8:11 says "I'm sorry i can't prounounce anything mb plez dont make fun of me thx" barely a frame.. my ocd nearly killed me

[@johnopalko5223]

Mine, too. I had to go back and single-step through it just so I could read it. FWIW, I couldn't find anything wrong with his pronunciation that couldn't be explained by his accent. Methinks the fellow is being too hard on himself.

[@hoodedR]

Got it on my first try xd... Guess I was lucky

[@UFO314159]

. = +1 frame; , = -1 frame.

[@BlehCatBark]

Me and my fellow student friends would definitely want a gamma function video!!

[@insaneweasel1]

Today I learned that's the worst time to watch an amazing video on complex math is after a gigantic meal that has put you in a food coma.

[@satyamprakash7030]

Thats precisely what happened to me

[@tmendoza6]

I am a returning student attempting a formal education in mathematics. It is horrible how many students just memorize, compute, and forget because they never get a chance to see the wounder and creativity of higher mathematics. your vids keep the alive!

[@chirayu_jain]

If first derivative represent the slope 2nd derivative : concavity Then what does 3rd, 4th and so on derivative represent. Please reply

[@ЧингизНабиев-э2г]

Chirayu Jain slope of the slope of the slope...

[@IcaroCamposdeAPinto]

This video reminds me of 3Blue1Brown. I like it.

[@vcubingx]

Thanks. I used his animation engine, which is why it looks so similar

[@scares009]

I've always wondered if there was something along the lines of fractional derivatives. I didn't know there would be actual applications for it!

[@RotatingBuffalo]

BROTHER WHAT ARE YOU DOING HERE WTF

[@scares009]

I'm a math nerd, what do you expect? :)

[@jafetriosduran]

It can be use in control theory for make controllers with greater degrees of freedom, it really different from the traditional calculus and the solution are non trivial, but it's a great subject

[@gunhasirac]

Jafet Ríos Durán that sounds very interesting. I just learned control theory and viscosity solution recently. Is there any recommended references?

[@jafetriosduran]

@@gunhasirac of course you can start with fractional calculos of Igor Podlubny and search about the Mittag Leffler function

[@matthewfuerst6456]

11:50 this is so freaky. Literally 2 days ago a video popped into my recommended about synchrous curves or something and I started thinking about what the derivative of that is. Started looking into cycloids and stuff but I haven’t really learned parametric graphing yet (Highschool junior) so there’s some prerequisites that I’m trying to get through at the same time. Now this video pops into my recommended that has the exact stuff that I’m looking for?

[@Jordan-jv6kl]

I’m glad you’re interested in this stuff, but be sure not to think of earlier math classes as just something you have to get through, they’re all important to understand :)

[@jbskmr]

The fractional derivative has many applications! Every battery and every medical implant electrode has impedance that involves a fractional derivative. Every capacitor responds fractionally, from its current to its failure lifetime. Only most engineers do not know enough math...

[@מידןטמיר]

I was sure I was the first to invent this in the 9th grade, but now I'm not sure my formula is correct

[@reinerwilhelms-tricarico344]

I like the smoothness of this presentation but there is still a disadvantage: in all the cool looking animated transformation of the formulas I find it really hard to actually follow: for this I would usually stop the video and try to convince myself that the currant formula follows from the previous one(s). But then the previous formula isn’t on the screen anymore. So I end up having to write everything down so I can actually verify each step. When you do these animated changes of the formulas, which are appealing and have a bit of a sense of wizardry, then why don’t you keep the previous formula on the screen?

[@igxniisan6996]

8:11, That sudden ghostly text you've been struggling to see what it is but it disappeared at light speed: *“I'M SORRY I CAN'T PRONOUNCE ANYTHING MB PLES DONT MAKE FUN OF ME THX”*

[@JaydentheMathGuy]

This is so beautiful. YOU U CAN HAVE ALL OF MY MONEY! COLLEGE CANNOT DO BETTER THAN THIS!

[@chirayu_jain]

Just amazing, I was searching this for months, and got this recommended. *subscribed*

[@lara.0783]

Thank you for explaining this, I found it very interesting and I like how you do things! I would be interested in watching a video about the gamma function, as I don't really have any acces to other sources and I like how you make this accessible to people, like me, that don't really know a lot about maths except for other KZbin videos!

[@gustawdaniel]

In 9:18 you can see oscillations of green function. I calculated that no oscillations should be there. Thank you for great and inspiring video. I am totally impressed.

[@vcubingx]

You are right, there shouldn't be any oscillations. But the way I animated it relied on numerical integration, resulted in the little oscillations of greens function you mentioned. Thanks for watching the video 😊

[@pierrelacombe4757]

This artefact is well known in digital sound processing... causing disturbing audio effects...

[@MaksProger]

I thought that actually takes place. So misleading. Thanks

[@thedoublek4816]

@@pierrelacombe4757 Gibb's Phenomenon?

[@peasant7214]

did you copy this from BpenRpen channel? :p btw im not obsessed with copy rights or anything. just saying. its always good that we learn, even things that are already discovered.

[@SirPlotsalot]

It's just thre same style

[@Schlaousilein67]

Cool, I've been interested in this for a few weeks.

[@Zxv975]

Wow, that elegant solution to the Tautochrone problem blew my mind. It's as if the solution just jumps out at you!

[@Jamiree7]

"The fractional calculus" by odham and spanier is a good book on the topic. Good work in the video! If you're interested in applications, "On the control and stability of variable-order mechanical systems" is a good paper that puts to use these concepts in control theory.

[@WillyyKW]

What kind of 3b1b is this?

[@maxs5022]

great vid! there is also a way to introduce fractional derivatives using multipliers in the Fourier domain. If you also know things about this, i would really enjoy a video comparing those two concepts.

[@umbreeniftikhar4446]

Yes a video on gamma function plz

[@omargaber3122]

i hope see the man who made this wonderfull and amazing vedio and after that he asked from the people not make fun of him. you should ask from people saying thanks . really i liked you

[@lPlanetarizado]

I knew you could solve that problem with variational calculus, but I didnt knew it relates to fractional derivates; by the way, there is a "logic" to solve the problem with fractional derivates? I just ask because they seems to be related, and dividing bt gamm function seems kind of random

[@vcubingx]

I think it's more of you need to look for the formula of fractional integral or derivative. Like in that case it was just missing the 1/gamma(n) part which is why we divided both sides my gamma(1/n).

[@zombiedude347]

If the function has a laplace transform, then I^n(f) equals L^-1(s^(-n)*L(f)).

[@victorribera5796]

Why the derivative in the animation of the evolution of the different fractional differintegrations when n equals -1 (the normal derivative) has like an overshoot near zero??

[@sohailmuhammadrafiq1053]

8:11 I'M SORRY I CAN'T PRONOUNCE ANYTHING MB PLES DONT MAKE FUN OF ME TNX

[@sankettikare1672]

Very interesting video and well explained.

[@vcubingx]

Glad you liked it!

[@mastershooter64]

Indian 3blue1brown nicee!

[@PedroTricking]

8:10 I was thinking that ceiling looks disgustingly horrendous but maybe it's just one of many branches and that's why the ceiling is there? Similar to how when you take a complex logarithm you chose the branch that gives you an angle between 0 and 2pi. 13:00 Why would that be true at all?

[@jvdcaki192]

Has anyone tried challenge 1? Im stuck. I tried using the same thing he does for n=2 but for n, not using induction as it is done in Wikipedia. I get to an expression which I have to relate to the n-th integral of f(x) but I cant see how

[@Bluemotion567]

Did you give credit to this article? It literally feels like you're reading it medium.com/cantors-paradise/fractional-calculus-48192f4e9c9f

[@carl13579]

Agree! Everything is in the same order, presented the same way, even the animation!

[@Dakkidaze]

He did mention it It's inside the description field, open the Google docs link in the source part and you will find it

[@kevindeng9735]

this got recommended in my facebook so here i am

[@vcubingx]

Wtf how

[@JamesLewis2]

Alternatively, using integration by parts with u=t and dv=f(t) dt, the term -int(t*f(t),t,0,x) becomes -x*int(f(t),t,0,x)+int(int(f(t),0,s),s,0,x), and then the x*int(f(t),0,x) term cancels out, showing that g=I^(2)f. Also, by analytic continuation, it turns out that the only values of z at which Gamma(z) is not defined are the non-positive integers, while if Im(z)≠0, Gamma(z) is defined, even if Re(z) is a non-positive integer; additionally, 1/Gamma(z) has only removable singularities (again, at non-positive integers), meaning that it can be extended to an entire function; it still isn't helpful for defining multiple differentiation, because at non-positive integers, this extension of 1/Gamma(z) is 0.

[@robfielding8566]

d[ d[x] / d[y] ] / d[x] = (d[d[y]] / (d[x] * d[x]) - (d[y]/d[x])*(d[d[x]] / (d[x] * d[x]) = d^2y/(dx^2) - (dy/dx)*(d^2x/dx^2) .... saying that "d^2y/dx^2" is not really the second derivative, because it assumes that (d^2x/dx^2) is zero, which it is not always. Explicitly calculating with d[] as an implicit diff operator is a simple way for differentials to divide normally. See Johnathan Bartlett. I think this bit of notation is responsible for a lot of what is complicated in calculus, that it's a notational white lie.

[@overlordprincekhan]

8:11 For those who are wondering what that splash transition texts say: I'M SORRY I CAN'T PRONOUNCE ANYTHING MB PLES DONT MAKE FUN OF ME THX

[@변상빈-s4j]

Thanks for awesome video, but i can't understand 7:25 part of index. i think d^n/dx^n (I^n f(x))= f(x). is it correct?? please teach me

[@praveenkumar.r3654]

It's a great video :-) really I like it very much. Within 15 mint u gave a small intro about Fractional calculus. Pls, upload more video related to Fractional derivative.

[@genericcandy]

There is one thing that i don't understand about fractional derivatives : based on the formula at 11:18, if you take the 3/2-derivative of th constant function 1, you get sonething that's nonzero. However, the 3/2-derivative is the 1/2-derivative of the 1-derivative, so the 3/2-derivative of 1 should be the 1/2 of 0, which is 0 by linearity of the D operator. So there is clearly a problem (it is zero and nonzero), what is the issue ? Is the "composition rule" (f^a * f^b = f^(a+b), a > 0, b > 0) true for I but not D ?

[@EstiagoGaming]

So your format is inspired by 3blue1brown

[@BorisNVM]

good video, I didnt know about that application.

[@vcubingx]

Glad you liked it!

[@Abhisruta]

Please give a video about gamma and beta function...great video for using MANIM...the next generation 3B1B...

[@Kram1032]

Is there anything interesting to be said about, like, the expeced value over all derivatives or something like that? Like, normally you get Integral g(x) f(x) dx (with definite borders) is the expected value of f with respect to g over a given interval, right? So how about Integral a I^a(x) da? - giving you back "the expected function" for some interval. - is this anything interesting?

[@andysolano7847]

After taking real analysis in my undergrad, on the last day I went up to my professor and asked him about fractional derivatives because it was a random thought that came to mind. “What is a 3/4ths derivative?, what about the Pi th derivative? What about a derivative that changes, like x in certain intervals the 3rd derivative is taken, but x in other intervals the 2nd derivative is taken? Or what if it changes constantly based on another function?”. He didn’t answer my question and told me I would learn that in graduate level analysis. Well I took real analysis again (grad level) and I didn’t learn any of that. Thanks for the video !!

[@markgraham2312]

9:17 to 9:22 visually explains everything. You should have started there and given an example of d^1/2 f / dx^1/2 for f(x) = mx + b. Make it simple to understand. [9:17, 9:22] does that visually. Now do it algebraically.

[@mickelilltroll77]

A real-world application: Loudspeakers. To create a model of the speaker that fits measured data, fractional derivatives are needed both for the visco-elastic 'rubber'-suspension and the voice-coil. The coil becomes lossy when it is surrounded by ferromagnetic material and the equation describing the relationship between the voltage and current over the coil gets a fractional derivative typically in the range [0.5 0.8].

[@bsharpmajorscale]

I've spoken English for 25+ years, and I can't pronounce most anything either. :P But manim is so cool. I wish I were mathier, because I'd totally make something with it, just for fun.

[@jessstuart7495]

Can fractional derivatives be treated as linear operators when they differ by integers? (Ex. Derivatives 1/2, 3/2, 5/2, ...)

[@Olydis]

Check out medium.com/@olydis/fractional-derivative-playground-74e61c28721f if you want to play with fractional derivatives interactively :)

[@WalterUnglaub]

7:50 Just a tiny nitpick, but the left dots in your graph should be open circles, no? (otherwise you have a one-to-many function)

[@HL-iw1du]

What about an analogue to the taylor series with an integral involving fractional derivatives?

[@hoodedR]

Woah that's bold... You mean expressing the taylor expansion not as a series over naturals but as a continuous integral over all +ve reals?

[@HL-iw1du]

Ranjan Bhat What’s +ve? But ya, like changing the taylor series from a sum to an integral. The result might not exactly equal the taylor series though, as turning sums into integrals often changes the value you get after evaluating them.

[@hoodedR]

@@HL-iw1du +ve... Positive..? Yeah just because we can create a Taylor expansion doesn't confirm its convergence. Or so I've been told

[@HL-iw1du]

Ranjan Bhat oh I see.

[@francoiswessels8062]

kzbin.info/www/bejne/gl7JnGyDrbmIr7s@@HL-iw1du​

[@pardeepgarg2640]

Fractional Calculus is somewhat harder than Normal Calculus , Also fractional integral and derivatives don't have locality You can see Vcubingx video on fractional Calculus

[@mimithehotdog7836]

12:58 ds/dy = sqrt(2g)/pi * T_0/sqrt(y) where g is gravity, s is function of y, what is T_0? T_0 = T{y_0} ?

[@davidbrown8763]

I am sure that this is a very importantly informative video. Sadly, however, in order to preserve my sanity, I could not watch to the end because of the unnecessary, distracting, annoying music - which is such a pity. I have never attended a lecture, where high concentration is needed, that was disrupted by music of any kind. By the way, I am a musician.

[@idontknowwhathandle2use]

4:00 Why would you use the Gamma Function? Wouldn't the Pi function be more convenient since it doesn't have the "n-1" and outputs the corresponding factorial for each value of n, without needing to add 1?

[@_DD_15]

Can you explain please, what does it mean geometrically to do the half derivative of 1? 1 is a constant, there is no variation. How is that explainable, derivatives are grotesquely said differences between values. If there's only one value, how can a derivative exist?

[@MoeSalamaIbrahim]

Some fluid dynamicists use fractional calculus to better understand viscoelasticity. It also arises in the modeling of RL and RC circuits and the time evolution of electric charge within the circuit. Applications do exist.

[@kalaivani162]

Do anyone have idea about emerging definition of fractional derivative? Apart from classical ones...

[@frankmccann29]

Gamma function will work for me. Thanks. You guys on KZbin are better than school. They need to teach Laws of Math furst b then show people how t I use math.

[@Thomas.P.C]

Great video! One criticism though is when you're manipulating the math don't animate what you're manipulating into the new equation. It's easy to get lost as to what you're doing and how we got there especially since we have to go back and replay what was originally on the screen and connect with what you're saying verbally to what's on our screens after.

[@morpholino]

There is application of the fractional integral in electrochemistry (e.g. see Bard and Faulkner’s book)

[@Entr0zy]

You completely ruined this video with the amount of adverts on here. was taking apart a phone and decided to give this a watch over 3blue1brown but its very hard to focus over the amount of adverts on here. wont be watching again. unsuscribed.

[@videos4mydad]

I liked this video, but I got to say at 2:12 and other places - there is no value at all in reading out a complex formula when it is visually on the screen. Use your voice to get to the deeper meaning or truth of the formulate that is NOT evident by just looking at the formula.

[@ClarkPotter]

"I'm sorry I can't pronounce anything MB. Please don't make fun of me. Thanks."

[@蒋正-k6u]

I think there is a tiny mistake in ur video. So at 7:14. The video is saying that the nth derivative of nth integral of a function is just the function itself, but it seems u wrote a extra "f" in the derivative. I don't if that's a mistake or not, i am just a 10th grader.

[@ezino]

Where is 3blue1brown. I feel he's trying to copy his format. Your idea is nice tho, love it.

[@Encorous]

Pls explain gammar function

[@nickmundy9052]

Yes pls ezplain

[@willyh.r.1216]

Derivative, Fractional Derivative, Rational Derivative, Irrational Derivative, Real Derivative, Complexe Derivative, etc.

[@DavyCDiamondback]

I can imagine statistical applications. That’s the thing about statistics, you just make up shit and measure information with as many different metrics as possible

[@calcal5135]

The factorial can be replaced by the gamma function but is this replacement unique? If not then fractional integration is not uniquely defined and neither is fractional differentiation.

[@virajsharma1654]

Let me be clear first I did not watched this video bust as a science student the thumbnail scared me. I know what Derivatives are and how to solve them but in fraction ooh boy it looks like pain to me

[@vikramtete7461]

Sir...what is the physical or geometrical meaning of fractional derivative?

[@theultimatereductionist7592]

11:04 Why would D^(1/2) evaluated at 1 equal a function of x? Did you mean D^(1/2) evaluated at x=1 equals 1/sqrt(pi)?

[@vcubingx]

nope what's on the screen is what I meant. The half derivative of a constant equals a function in terms of x. Quite intriguing!

[@MrNosterp]

This is actually some great content but you really are dangerously close to encroaching on 3b1bs videos. I hope he doesn't mind.

[@shrishtyjain9281]

This video is very helpful. Please can u make a video on Caputo fractional derivative?