Fractional calculus in Physics?

In summary, the conversation discussed the use of fractional calculus in physics, particularly in the quantization of non-polynomial Hamiltonians in quantum mechanics. The speaker also mentioned the potential meaning and utility of fractional calculus in physics, such as canceling infinities in perturbation calculations. However, the other person in the conversation was not familiar with the term "fractional calculus" and clarified that they had only heard of variational calculus. The conversation also touched on the definition of a polynomial Hamiltonian and whether it includes variables that are powers of non-integer numbers. The speaker provided a link to further information on fractional calculus.
  • #1
eljose79
1,518
1
Has any menaing the use of fractional calculus in..physics?.i have used it several time to quantizy non-polynomial hamiltonians in quantum mechanics...(such us H=p**e e not an integer).but does the fractional calculus have a meaning or utility in physics?..to cancel infinities to calculate perturbation corrections or all that...
 
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  • #2
Do you mean 'variational calculus?' I'm afraid I've never heard the term 'fractional calculus.'

Also, I've never once seen a polynomial Hamiltonian. ;)

- Warren
 
  • #3
answer..

Sorry..perhaps it was my bad english..when i meant "polynomial" i mean hamiltonians of the form...

H**2=Px**2+Py**2+.. or H=Px**2+Py**2..that is the variables E and P,s appear in that way (the powers are always integer).


By fractional calculus it is mean that instead of using the operator (d/dx)**n being n and integer n can be real or even complex you can take a look about it in www.mathworld.com
 

1. What is fractional calculus?

Fractional calculus is a branch of mathematics that deals with integrals and derivatives of non-integer orders. It extends the traditional concepts of calculus to non-integer values, allowing for a more precise and accurate representation of physical systems.

2. How is fractional calculus used in physics?

Fractional calculus is used in physics to model and analyze complex systems that exhibit non-integer behavior, such as in fluid mechanics, quantum mechanics, and electromagnetism. It allows for a more comprehensive understanding of these systems and can provide more accurate predictions.

3. What are some real-world applications of fractional calculus in physics?

Fractional calculus has been applied in various fields of physics, such as in the study of viscoelastic materials, diffusion processes, and fractional quantum mechanics. It has also been used to analyze and predict the behavior of complex networks and chaotic systems.

4. How does fractional calculus differ from traditional calculus?

Traditional calculus deals with integrals and derivatives of integer orders, while fractional calculus extends these concepts to non-integer orders. This allows for a more precise and detailed analysis of systems that exhibit non-integer behavior.

5. What are the advantages of using fractional calculus in physics?

The use of fractional calculus in physics allows for a more accurate and comprehensive representation of complex systems, leading to better predictions and a deeper understanding of physical phenomena. It also provides a more flexible and versatile approach to modeling various systems, making it a valuable tool for scientists and researchers.

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