Function Repository Resource:

# FractionalIntegrate

Calculate fractional integrals

Contributed by: Sami Yrjänheikki
 ResourceFunction["FractionalIntegrate"][f,{x,α}] gives the α-fractional integral of the function f with respect to variable x.

## Details and Options

If α=1, ResourceFunction["FractionalIntegrate"][f,{x,α}] is equivalent to Integrate[f,x].
ResourceFunction["FractionalIntegrate"] uses the formula .

## Examples

### Basic Examples (2)

Semi-integral of 2x:

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Taking the semi-integral twice yields the standard antiderivative:

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### Scope (5)

If α=1, the result is the usual integral:

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Semi-integral of elementary functions:

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Semi-integral of trig functions:

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Semi-integral of inverse trig functions:

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More exotic fractional integrals:

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### Possible Issues (1)

Not all integrals can be computed:

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Sami Yrjänheikki

## Version History

• 1.0.0 – 04 May 2020