Fractional-order Derivative

In recent years, fractional calculus has attracted many mathematicians and researchers in different fields: Maths, Physics, Astronomy, and Engineering.
This is an introductory and motivational video for fractional calculus. In this 7 min lecture, I showed how to find the fractional-order derivative of a simple power function. For instance, half-order derivative of f(x) = x.
Book References:
1) The Variable Order Fractional Calculus of Variation. Springer 2019 by Almeida, R. and Tavares, D. and Torres, D.F.M.
2) Fractional Differential Equations, Academic Press 1999 by Podlubny, I.
3) Introduction to Fractional Differential Equations, Springer 2019. By by Constantin, M. and Gheorghe, D. and J. Tenreiro, M.},
4) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley 1993. By Miller, K.S. and Ross, B.
5) Measure Theory and Fine Properties of Functions. CRC Press 2015. By Evans, L. C. and Gariepy, R. F.},
6) Functional Fractional Calculus. Springer 2011. By Das, S.
7) The Analysis of Fractional Differential Equations. World Scientific 2014. Herrmann, R.

[@kgnaneshwar1114]

It is good video to understand about fractional order derivative

[@redgreenblue123]

Thanks!

[@EasyMathWithIbrahim]

Very good presentation. Go ahead. Best wishes.

[@gems759]

Thanks

[@redgreenblue123]

Thank you so much 😀

[@shawonshimu7088]

very easy to understand the fractional-order derivative :)

[@redgreenblue123]

Thanks!

[@shukuralammozumder3563]

great to see

[@ibrahimrupom9337]

Smart presentation. Thanks

[@redgreenblue123]

Thanks!

[@colorizedenhanced-silentmo3068]

Good evening, Mujib Chowdhury. this is extremely okay video. thanks. :)

[@redgreenblue123]

Good morning!

[@AbdurRahman-qj7em]

Well, explained.

[@redgreenblue123]

Thanks!

[@nikhils216]

V Good Explanation..Pls upload more videos on Fractional Calculus.

[@redgreenblue123]

Thank you

[@randompacifist3157]

Thanks sirr!

[@MDHasan-en7ly]

A good video. Thanks

[@redgreenblue123]

Thanks!

[@dr.mdsazzad9878]

nice to see

[@redgreenblue123]

Thank you

[@anjani8594]

sir your explanation is very good..... if fractional order de has power 1 it's equal to normal ode or not?

[@azzteke]

?

[@gems759]

simple answer is yes. You can verify it by plugging alpha = 1. However, unlike definition of ordinary derivative, the definition of fractional derivative is not unified yet. There are couple of definitions of fractional order such as GL, Caputo etc.

[@sandorszabo2470]

This result is incorrect, misleading. "In recent years" is about 100 years or so. I very recommend to search the literature. Unfortunately also there are a lot of misconception. Only the very beginning of the video is correct, where it is mentioned RL, Caputo, GL.

[@sheikhhasan5532]

What's the correct result? He mentioned the example was derived in 1819.

[@sandorszabo2470]

@@sheikhhasan5532 He mentioned, correctly, that there are 3 definitions. After that we see an idea, an analogy, which is motivating, but not a correct proof. He made calculation without precise definition. Not my task to derive the correct result. As a good starting point I suggest wikipedia.

[@redgreenblue123]

Dear @@sandorszabo2470, Thank you for watching my video and making comments! I love to have corrections :) Now let's talk about your concern/comments. First of all, I didn't present anything from my own. I mentioned I didn't follow any definition. I just gave an example that Lacroix derived in 1819. You can check the book references I have listed in the description box. If you can prove Lacroix's example is wrong/ or find an error, I will be happy to learn from you :)

[@sandorszabo2470]

@@redgreenblue123 At 4:12. What is this equality? Definition or theorem?

[@redgreenblue123]

@@sandorszabo2470 Very simple thing. One of the properties of the Gamma function.