Can Fractional Calculus Handle Derivatives of Non-Integer Orders?

  • Thread starter batsan
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In summary, the conversation discussed searching for literature on solving derivatives with orders between 0 and 1. The suggestion was made to search on Google and Wikipedia, although caution was advised when using Wikipedia as a source. The OP was also encouraged to explore textbooks listed in the references on the Wikipedia page.
  • #1
batsan
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I'm searching literature for solving derivative with order between 0 up to 1.
If anybody have that, please post me!
 
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  • #2
There are books on the subject. I have one, but i can't remember the title. In these cases google is your friend.
 
  • #4
DeadWolfe said:
As always, wikipedia knows all:

http://en.wikipedia.org/wiki/Fractional_calculus

Be wary about learning a subject from Wikipedia, since it is not written by experts (this has been talked about quite a lot recently on this forum; do a search if you're interested in reading what others have to say on the matter)

To the OP: Why not look into some of the textbooks listed in the references on that Wikipedia page.
 

FAQ: Can Fractional Calculus Handle Derivatives of Non-Integer Orders?

What is a non-integer order derivative?

A non-integer order derivative is a type of mathematical operation that calculates the rate of change of a function at a specific point, but with a non-integer exponent. This means that instead of taking the first, second, or third derivative (exponents of 1, 2, or 3), it takes a fractional or decimal exponent, such as 1.5 or 2.3.

Why do we need non-integer order derivatives?

Non-integer order derivatives have applications in various fields such as physics, engineering, economics, and biology. They allow for a more accurate and precise description of systems that exhibit non-integer behavior, such as diffusion, fractals, and viscoelastic materials.

How are non-integer order derivatives calculated?

There are several methods for calculating non-integer order derivatives, including the Grunwald-Letnikov, Riemann-Liouville, and Caputo derivatives. These methods use different approaches, but they all involve taking the limit of a ratio of differences as the interval between points approaches zero.

What is the difference between a non-integer order derivative and a fractional derivative?

A non-integer order derivative and a fractional derivative are often used interchangeably, but there is a subtle difference between the two. A non-integer order derivative can have any real number as its exponent, while a fractional derivative specifically has a fraction as its exponent, such as 3/2 or 5/3.

Can non-integer order derivatives be negative?

Yes, non-integer order derivatives can be negative. The sign of a non-integer order derivative depends on the direction of the function's curvature at the specific point being evaluated. If the function is concave down, the derivative will be negative, and if it is concave up, the derivative will be positive.

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