Fractional Differential Equations

In summary, the conversation was about finding internet leads on the topic of Fractional Differential Equations and how they relate to Tsallis's Non-Extensive entropy. The suggested websites were fracalmo.org and arxiv.org, but there were some difficulties with the latter. The main goal was to find a correlation between fractional DEs and Tsallis's statistics.
  • #1
polyb
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Hello all!
I was wondering if anyone knew of any good internet leads(besides mathworld, which does not have that much) on the topic of Fractional Differential Equations. I am wanting to investigate Tsallis's Non-Extensive entropy and from what I have come to understand he came to his generalized statistics through fractional DEs. Actually I would prefer something would correlate the two.

If you have any ideas please pass them along! Thanks in advance!
polyb
 
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  • #3
Thanks benorin!

falcalmo.org seems like it might provide some good links. I have had some trouble with the arxivs lately, seems either the server is not responding and/or it seems that Tsallis's papers have been reduced. That or I am not doing something right! Plus most of the papers I found under the search criterea for Fractional DEs seems to be more specified to particular problems and not the generalized approach I have been seeking, specifically how it relates to Tsallis's generalized statistics. Oh well, keep trying!

Once again, thanks!
 
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What is a fractional differential equation?

A fractional differential equation is a type of differential equation in which the derivative of a function is a fractional order. Instead of using integer orders (such as 1st, 2nd, or 3rd order), fractional orders (such as 0.5, 1.5, or 2.5) are used to describe the rate of change of the function.

What is the significance of fractional differential equations?

Fractional differential equations have a wide range of applications in various fields, including physics, engineering, biology, and finance. They provide a more accurate description of real-world phenomena that cannot be fully captured by traditional integer-order differential equations.

How are fractional differential equations solved?

There are various methods for solving fractional differential equations, including numerical methods, power series methods, and Laplace transform methods. However, due to the complexity of these equations, exact solutions are not always possible and approximate solutions are often used.

What are some examples of fractional differential equations?

Some examples of fractional differential equations include the fractional heat equation, fractional wave equation, and the fractional diffusion equation. These equations are commonly used to model heat transfer, wave propagation, and diffusion in materials with non-integer properties.

What are the challenges in studying fractional differential equations?

One of the main challenges in studying fractional differential equations is the lack of well-established analytical methods for solving them. This makes it difficult to obtain exact solutions, and numerical methods are often used instead. Additionally, the non-local nature of fractional derivatives can make it challenging to interpret the physical meaning of the solutions.

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