Fractional calculus - uses, examples?

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Discussion Overview

The discussion centers around the applications and interpretations of fractional calculus, specifically fractional derivatives and integrals. Participants explore its uses in various fields, particularly in physics and engineering, while seeking specific examples and insights into its complexity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses curiosity about the applications of fractional derivatives and integrals, noting a previous conversation with a professor that left them without clear answers.
  • Another participant asserts that there are numerous applications of fractional calculus and suggests that the interest may guide the discussion on specific uses.
  • References to specialized journals and books on fractional calculus are provided, indicating a wealth of literature available for further exploration.
  • A later post reiterates the initial inquiry about specific physics problems that necessitate the use of fractional calculus.
  • One participant mentions that fractional calculus can generalize basic physical concepts such as inductance, resistance, and capacitance, particularly in the context of electrical networks involving Constant Phase Elements (CPE).

Areas of Agreement / Disagreement

Participants generally agree that fractional calculus has many applications, but there is no consensus on specific examples or problems where it is particularly necessary. The discussion remains open-ended with multiple viewpoints and inquiries.

Contextual Notes

Some limitations in the discussion include the broad nature of the initial question regarding applications, which may lead to varied interpretations and responses. Additionally, references to literature may not cover all potential applications or contexts.

elegysix
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Does anyone know any applications / uses for fractional derivatives and integrals?

I supposed the idea and asked a professor, he tried to explain fractional calculus to me, but I was in calculus 2 at the time... so it was way over my head back then. I asked him what it could be used for and he didn't really give me an answer, just that it was too complex to explain lol.

Now, 3 years later, I'm looking back on it and wondering what a fractional derivative can be interpreted as, and what it could be used for. Anyone have some insight?
 
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Way too many to count. What interests you?

We have three specialized journals:
  1. Fractional Calculus and Applied Analysis
  2. Fractional Differential Equations
  3. Communications in Fractional Calculus.
Of which the second is applications based.

I highly recommend Podlubny's book Fractional Differential Equations, or West's book Physics of Fractal Operators as they both have a chapter on applications. Also http://people.tuke.sk/igor.podlubny/fc_resources.html" is really good place to start.
 
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Thanks, I'll check those out.

I think asking how to use it is too broad of a question,
is there like a specific physics problem where you need to use it?
 
elegysix said:
Does anyone know any applications / uses for fractional derivatives and integrals?

I supposed the idea and asked a professor, he tried to explain fractional calculus to me, but I was in calculus 2 at the time... so it was way over my head back then. I asked him what it could be used for and he didn't really give me an answer, just that it was too complex to explain lol.

Now, 3 years later, I'm looking back on it and wondering what a fractional derivative can be interpreted as, and what it could be used for. Anyone have some insight?

Some references are provided page 5 in a paper written for general public "La dérivation fractionnaire" :
http://www.scribd.com/JJacquelin/documents
(Sorry, not translated yet).
There are a lot of applications for fractionnal calculus. One of them is the genertalization of the basic physical notions of Inductance, Resistance, Capacitance. A very useful generalization for the calculus of impedance of some electrical networks, especialy in case of presence of CPE in it (Constant Phase Element) :
 

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