- #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!
If anybody have that, please post me!
DeadWolfe said:
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.
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.
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.
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.
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.