# Fractional Euler-Lagrange equation [closed]

Using Mathematica, I need to perform the derivation of the fractional Euler-Lagrange equation as derived in this article.

Regarding this, I searched many links, but I was not able to master the concepts required to start writing the code. I don't seem to have the knowledge needed to search for code in Mathematica.SE effectively.

It would be very helpful if someone would please suggest to me any coding related to my topic.

• Can you please: Include all relevant details in the question so people don't have to read a paper to be able to answer; Show what you tried already. Dec 12 '19 at 7:52

Since you mentioned that you don't know what to look for and even search this site, hopefully this will be a starting point.

You need to check the variational methods. Here are some links variational derivative and Euler-Lagrange equations and here you can find more variational methods.

Minimal working example is the following

Needs["VariationalMethods"]
EulerEquations[
1/2 m r^2 θ'[t]^2 + m g r Cos[θ[t]], θ[t], t]
DSolve[%, θ[t], t]
`

which is the simple pendulum described by

$$\mathcal{L} = \frac{1}{2} m r^2 \dot{\theta}^2 + mgr \cos \theta$$

• It seems these are fractional variants, I wonder how much the normal solution routes differ Dec 12 '19 at 16:29
• @CATrevillian That is something I am not familiar with, and as I said the reply was supposed to be just an introductory exposition to variational methods and a simple example verifying that all is well :) Dec 13 '19 at 7:36