Function Repository Resource:

# FractionalD

Calculate a fractional derivative

Contributed by: Sami Yrjänheikki
 ResourceFunction["FractionalD"][f,{x,α}] gives the fractional derivative .

## Details and Options

If α is an integer, ResourceFunction["FractionalD"][f,{x,α}] is equivalent to D[f,{x,α}].
The Cauchy method uses the formula .
The Caputo method uses the formula .

## Examples

### Basic Examples (2)

Half-derivative of x2:

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Taking the half-derivative twice yields the usual first derivative:

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### Scope (5)

If α is an integer, the result is the normal derivative:

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Half-derivative of elementary functions:

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Half-derivative of trig functions:

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Half-derivative of inverse trig functions:

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A more exotic fractional derivative:

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### Options (1)

#### Method (1)

Choosing between Cauchy and Caputo may result in performance differences:

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### Possible Issues (1)

FractionalD uses integration under the hood. Sometimes the integral cannot be computed:

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### Neat Examples (1)

The fractional derivative smoothly interpolates between the function and its derivative:

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Sami Yrjänheikki

## Version History

• 1.0.0 – 15 April 2020